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•^r^RST  PRINCIPLES  OF   NATURAL   PHILOSOPHY 

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r~  I  AHIS  little  volume  has  been  prepared  for  your  con- 
-*-  venience  and  not  for  that  of  your  pupils.  It  is 
sent  forth  by  the  author  with  the  hope  that  it  may  lessen 
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notifying  him  of  any  errors  you  may  find  in  it,  or  in  the 
text-books  to  which  it  pertains. 

If,  in  your  class,  you  use  The  First  Principles  of 
Natural  Philosophy,  you  will  find  it  to  your  advantage 
to  have  a  copy  of  The  Elements  of  Natural  Philoso- 
phy and  habitually  compare  the  corresponding  topics. 
As  the  general  arrangement  of  the  two  books  is  the 
same,  the  reference  will  be  easily  made.  Such  reference 
being  made,  you  will  naturally  refer  to  the  corresponding 
notes  on  The  Elements,  contained  in  this  volume. 

If  your  class  uses  The  Elements,  you  will  still  find 
it  of  advantage  to  have  a  copy  of  The  First  Princi- 
ples, to  which  frequent  references  are  made  in  this  vol- 
ume. 


769793 


FIRST  PRINCIPLES 

OF 

NATURAL  PHILOSOPHY.,- 


CHAPTER  I. 

%9T  Tfte  full-faced  numeral*  at   the  left  of  the  page   refer  to  par- 
agraph* i  a  the  text-book. 

4.  "At  its  ordinary  pressure,  the  atmosphere  is  not  very  dense, 
and  its  recognition,  as  a  constituent  of  the  world  of  matter,  is  quite 
a  modern  notion.  It  would  seem  that  when  divided  by  a  million,  s« 
little  matter  will  be  left  that  we  may  justifiably  neglect  the  trifling 
residue  and  apply  the  term  vacuum  (§  187)  to  the  space  from  which 
the  air  has  been  so  nearly  removed.  To  do  so,  however,  would  be  a 
great  error,  attributable  to  our  limited  faculties  being  unable  to  grasp 
high  numbers.  It  is  generally  taken  for  granted  that  when  a  num- 
ber is  divided  by  a  million  the  quotient  must  necessarily  be  small, 
whereas  it  may  happen  that  the  original  number  is  so  large  that  its 
division  by  a  million  seems  to  make  little  impression  on  it.  Ac- 
cording to  the  best  authorities,  a  bulb  like  the  one  before  you  (13.5 
centimeters  in  diameter,  see  Appendix  B)  contains  more  than 
1000000  000000000000000000  (=1084)  molecules.  Now,  when  ex- 
hausted to  a  millionth  of  an  atmosphere  we  still  have  1  000000  000000- 
000000  (=1018)  molecules  left  in  the  bulb — a  number  quite  sufficient 
to  justify  me  in  speaking  of  the  residue  as  matter. 

"To  suggest  some  idea  of  this  vast  number,  I  take  the  exhausted 
bulb  and  perforate  it  by  a  spark  from  the  induction  coil  (£  300).  The 
spark  produces  a  hole  of  microscopical  fineness,  yet  sufficient  to 
allow  molecules  to  penetrate  and  destroy  the  vacuum.  The  inrush 
of  air  impinges  against  the  vanes  (see  Elements  of  Nat.  Phil.,  Fig. 
1 77)  and  sets  them  rotating.  Let  us  suppose  the  molecules  to  be  of 
such  a  size  that  a  hundred  millions  could  enter  in  every  second  of 
time.  How  long,  think  you,  it  would  take  for  this  small  vessel  to 
p't  full  of  air?  An  hour?  A  day?  A  year?  A  century?  Nay, 
almost  an  eternity!     A  time  so  enormous  that  imagination  itself 


6  [First  Principles  of  Natural  Philosophy,  p.  2.\ 

cannot  grasp  the  reality.  Supposing  that  this  exhausted  glass  bulb, 
indued  with  indestructibility,  had  been  thus  pierced  at  the  birth  of 
the  solar  system  ;  supposing  it  to  have  been  present  when  the  earth 
was  without  form  and  void ;  supposing  it  to  have  borne  witness  to 
all  the  stupendous  changes  evolved  during  the  full  cycles  of  geologic 
time,  to  have  seen  the  first  living  creature  appear  and  the  last  man 
disappear  ;  supposing  it  to  survive  until  the  fulfillment  of  the  math- 
ematician's predion  >.i  tint  the  sun,  the  source  of  energy,  four  million 
centuries  from  its  formation,  will  ultimately  become  a  burnt  out 
cinder  ;  supposing  ail  this — a;t  the  rate  of  filling  I  have  just  described, 
4  hundred  million  molecules  a  second,  this  little  bulb  even  then 
would  scarcely  have  been  filled. 

u  But  what  will  you  say  if  I  tell  you  that  all  these  molecules  will 
enter  through  the  microscopical  hole  before  you  leave  this  room. 
The  hole  being  unaltered  in  size  and  the  number  of  the  molecules 
undiminished,  this  apparent  paradox  can  be  explained  only  by  sup- 
posing the  size  of  the  molecules  to  be  diminished  almost  infinitely, 
so  that  instead  of  entering  at  the  rate  of  100  000  000  a  second  they 
troop  in  at  the  rate  of  something  like  300  003000  000000000000  a 
second." — WUliara  Crookes. 

It  is  estimated  that  a  cubic  centimeter  of  air  contains  about 
.000  000000  000000  000000  molecules.  Then  the  bulb  above  de- 
scribed would  contain  (13.53  x  0.5236  x  1000  000000  000000  000000 
=)  1 288252  350000  000000  000000  molecules  of  air  at  the  ordinary 
atmospheric  pressure.  When  exhausted  to  a  millionth  of  an 
atmosphere,  the  bulb  still  contains  1  288252  350000  000000  mole- 
cules, leaving  1  288251  061747  650000  000000  to  enter  through  the 
perforation.  At  the  rate  of  100  000000  molecules  a  second,  the 
time  required  for  them  all  to  enter  will  be 

12882510617476500  seconds,  or 

214708510291275  minutes,  or 

3578475171521  hours,  or 

149103132147  days,  or 

408501731  years. 

6.  See  Daniell's  "  Principles  of  Physics,"  pp.  222-236. 


[Fvrst  Principles  of  Natural  Philosophy,  pp.  23-81.]  7 

43.  See  note  on  §  4. 

Review  Questions,  Page  2&, 

1.  See  line  preceding  Exp.  1. 

2.  See|§land  8,  b. 

3.  The  kinds  of  atoms.     §  3,  a. 

4.  Eight  cubic  inches.    §  19. 

6.  Float  the  cork  on  the  water ;  surround  it  with  the 
larger  end  of  the  chimney ;  cover  the  smaller  end  with 
the  fleshy  part  of  the  hand  and  push  the  glass  downward 
into  the  water. 

7.  (a.)  An  atom,    (b.)  A  molecule. 

8.  Elementary.     §§  3  (a)  and  4  (b). 

9.  Compound.     §§  3  (a)  and  4  (b). 

11.  Same    size.      Vaporization   is  a  physical    change. 

§  11  (a). 

16.  See  §§  7,  30. 
19.  See  §  23. 

54.  The  momenta  of  the  blocks  mentioned  in  Exp.  29 
vrill  be  equal. 


8  [First  Principles  of  Natural  Philosophy,  pp.  35-36.] 

Exercises,  Page  85, 
25  x  100   _ 
Z'    "21T60"  ~      ' 

3.  1000  +  50  =  20. 

4.  The  canoe,  because  the  momentum  of  a  body  at  rest 
u  zero.     §  49. 

5.  5  x  4  =  10  x  2.     Their  momenta  are  equal. 

6.  Reduce  the  velocities  to  feet  per  minute. 

5 
*B 

i  x  m^  x  u 


=  5. 


n  x  n  x  < 

4 

7.  No. 

8.  (#.)  Physical.  (5.)  Chemical.  See  Hand  Book  note 
on  §  634  of  Elements  of  Nat.  Phil,  (c.)  The  molecule. 
(§  11,  a.) 

9.  Crowded  more  closely  together  on  the  concave  side  ; 
palled  further  apart  on  the  convex  side. 

10.  See  §  40  (a)  and  (b).  The  velocity  with  which  it 
strikes  will  depend  upon  the  distance  it  has  fallen.  §§  79 
(1)  and  98  (a). 

11.  The  momenta  must  be  the  same,  for  equal  forces 
produce  equal  effects.  Since  the  momenta  are  equal  the 
1100  pounds  will  move  twice  as  fast  as  the  2200  pounds. 

60.  Compare  Elem.  Nat.  Phil,  §  100. 


First  Principles  or  Haturcu  Philosophy,  pp.  M-60.]  9 

Exercise*,  Fnge  44. 

1.  §§  72,  73. 

2.  §  73.  The  base  of  the  sphere  is  a  point.  The  line 
of  direction  will  not  pass  through  this  point  unless  the 
supporting  surface  be  horizontal. 

5.  Doubling  the  weight  means  doubling  its  attraction 
(for  the  earth  or  anything  else). 

6.  One  unit.     §  60  (2). 

7.  To  the  outermost  bounds  of  the  universe. 

Exercises ,  Page.  50, 

1.  S  =  \gfl  =  16.08  x  100  =  1608. 

2.  v  =  gt  =  32.16  x  4  =  128.64. 

3.  s  =  iff  (2t  -  1)  =  16.08  (8  —  1)  =  112.56. 

4.  s  =  iff  (2t  —  1)  +  25  =  144.72  +  25  =  169.72,  the 
number  of  feet. 

5.  In  this  case,  the  increment  of  velocity  due  to  gravity 
(ff)  is  10  feet  instead  of  32.16  ft,  as  it  would  be  were  this 
a  freely  falling  body.  Use  the  same  formula,  giving  ff  thic 
new  value. 

v  =  gt  =  10  x  10  =  100. 

6.  It  is  9.81  meters,  or  981  centimeters. 

7.  The  first  one  has  fallen  for  5  sec. : 

S=igP  =  16.08  x  25  =  402. 
The  other  has  fallen  for  2  seconds : 

S  =  igt2  =  16.08  x    4  =    6132 

337  68 

8.  v  =  gt.    .'.  98.1  =  9.81/.    .'.  10  =  t. 

9.  S  represents  "  the  distance  traversed  by  a  freely  falling 
body  during  any  number  of  seconds";  \g  represents 
44 16.08  feet,  or  4.9  meters";  t2  represents  "the  square  of 
the  number  of  seconds,"  and  the  method  of  writing  the 
factors  {  g  and  P  represents  "  multiplied  by." 


10         [First  Principles  of  Natural  Philosophy,  pp.  56-65.] 

Exercises,  Page  56. 

1.  It  will  vibrate  the  same  number  of  times. 

2.  The  other  is  40  inches  long.     §  88. 

3.  They  will  vibrate  at  the  same  rate.  §  87.  Distinguish 
between  the  true  length  and  the  apparent  length  as  ex- 
plained in  Exp.  38.    See  Elem.  Nat.  Phil.     §§  141,  142. 

4.  Vl6  :  a/64  =1:2.  The  short  pendulum  will  vi- 
brate twice  as  fast  as  the  long  one.     Ans.,  8  times. 

5.  Make  it  one  ninth  as  long. 

6.  It  is  too  long.     Lower  the  bob. 

7.  Vi  :  V9  -'  2  °  '*.  The  short  one  will  make  three 
while  the  long  one  is  making  two. 

8.  V49  :  V64  =  7:8.  The  time  of  vibration  of  the 
long  pendulum  will  be  f  that  of  the  short  one.  (Its  num- 
ber of  vibrations  in  a  given  time  will  be  only  -J  that  of  the 
short  one.) 

9.  Four  times  the  length  of  the  second's  pendulum,  or 
(in  this  latitude)  about  156.4  inches  (more  than  13  ft). 

10.  One  fourth  the  length  of  a  second's  pendulum,  or  a 
little  less  than  10  inches.  Such  pendulums  are  very  com- 
mon in  clocks. 

Exercises,  Page  65. 
,    100  000x198       1A     -1    ,  ,  .,   .. 

L  "33000-^60"  =  10-    W°rk  by  cancellatlon' 
0    2000x10x50      500     ■  --j.     ,  .        *     .     , 

2*       33000x2      =  W  =  l0 A'  the  nUmber  °f  mmuteS* 

3.  Double  it ;  the  K.  E.  varies  with  the  square  of  v.    §  98. 

4.  They  are  equal. 

6.  5  x  20  x  50  =  5000,  the  number  of  foot-pounds. 

7.  (a.)  5000  foot-pounds,  (b.)  The  kinetic  energy  ex- 
pended in  lifting  them  to  an  elevation  of  50  ft.  was  all 
stored  in  the  bricks  at  that  height,  as  potential  energy. 

a  k. m.  =  St  =  ^o_xm ^200  =  40 000 000< 

2g  64.32 


[First  Principles  of  Katural  Philosophy,  pp.  66-77.]        11 

Review  Questions,  I*af/e  66, 

I.  Gravitation  pulls  downward  both  the  cork  and  the 
water.  But,  the  water  being  the  heavier,  is  drawn  with 
the  greater  force.  The  water  is,  therefore,  drawn  under 
the  cork  (it  having  freedom  of  molecular  motion,  §  39) 
and  pushes  the  cork  upward. 

3.  Because  the  centre  of  gravity  is  lower  ;  the  base  is 
the  same  ;  the  line  of  direction  is,  therefore,  less  easily 
thrown  without  the  base.     §  73. 

4.  At  the  bottom;  to  bring  the  centre  of  gravity  as  low 
as  possible. 

5.  Because  the  base  is  broader.     §  72. 

6.  No.  There  would  be  nothing  to  offer  any  resistance 
to  any  effort  that  he  might  wish  to  make.  There  would 
be  nothing  to  react  on  him  and  put  him  in  motion.  §  54. 
An  infinitesimal  force  from  without  would  move  him,  but 
he  can  not  exert  even  such  a  force  because  there  is  nothing 
upon  which  to  exert  it. 

7.  Quartered. 

9.  Because  of  their  freedom  of  molecular  motion. 

10.  Elasticity  in  particular. 

II.  Elasticity  of  the  spring. 

12.  If  the  nail  is  smooth,  adhesion;  otherwise,  cohesion 
aids. 

13.  To  bring  the  centre  of  gravity  as  far  below  the  centre 
of  buoyancy  (§  163,  b)  as  possible,  and  thus  keep  the 
vessel  in  stable  equilibrium. 

14.  Adhesion. 

15.  Gravitation,  of  which  gravity  is  a  special  kind. 

Exercises,  Page  77* 

1.  1000  -r-  100  =  10.— Ans. 

2.  To  put  the  unloaded  lever  in  equipoise. 

3.  The  two  arms  are  respectively  1  foot  and  4  feet  long. 
7  pounds  x  f  =  28  pounds. — Ans. 


12         {First  Principles  of  Natural  Philosophy,  pp.  77-85.] 

4.  The  two  arms  are  respectively  1  foot  and  5  feet  long 
7  pounds  x  f  =  35  pounds. — Ans. 

5.  The  two  arms  are  respectively  5  feet  and  1  foot  long 
7  pounds  x  -J  =  1  lb.,  6f  oz. 

G.  Not  in  the  middle,  because  then  the  arms  would  be  of 
equal  length  and  the  power  would  equal  the  load.  As  the 
power  is  only  half  the  load,  the  power  arm  must  be  twice 
as  long  as  the  weight  arm.  The  fulcrum  must  be  50'inches 
from  the  load  and  25  inches  from  the  weight.  (This 
ignores  the  weight  of  the  lever  itself,  or  assumes  it  to  be 
in  equipoise  about  the  fulcrum  placed  as  described.) 

7.  (a.)  18  ft.     (b.)  12  ft.     (c.)  12  ft. 

9.  The  power  (applied  at  c)  moves  10  inches. 
The  load  (applied  at  b)  moves  \  inch. 

As  the  power  moves  20  times  as  far  as  the  load,  the  load 
will  be  20  times  as  great  as  the  power.  §  108  (2).  100C 
lb.  x  20  =  20000  lb. 

Exercises,  Page  85, 

1.  5  :  1  =  125  :  25. 

2.  The  power  (applied  at  the  handle)  moves  9  ft.  while 
the  load  (suspended  from  the  rope)  moves  3  ft.  As  the 
power  moves  3  times  as  far  (or  3  times  as  fast)  as  the  load, 
the  load  must  be  3  times  as  great  as  the  power  when  the 
machine  is  in  equilibrium.     §  108,  (2)  and  (3). 

3.  The  radius  of  the  wheel  is  8  ft;  that  of  the  axle, 
1  ft.  Therefore,  the  power  will  be  \  of  the  load.  4000  lb. 
-$•..8  =  500  lb.  This  power  being  furnished  by  4  men, 
each  man  pushes  (or  ought  to  push)  with  a  force  of  125  lb« 
500  -*■  4  =  125. 

4.  (a.)  10  1b.     (b.)  20  1b.      (c.)  60  1b.     (d.)  30  1b. 

7.  2*        [  Z  ll  i" 


[First  Principles  of  Natural  Philosophy,  p.  93.]  13 

i;.ierrisrs,    I'(ff/r  U'.i. 

1.  The  weight  of  the  plunk  is  practically  at  its  centre  of 
gravity,  10  ft.  from  either  end.  Lifting  this  weight  at  one 
end  of  the  plank,  the  boy  is  using  a  lever  of  the  second 
class  with  arms  of  10  ft.  and  20  ft.  respectively.  Hence 
he  lifts  only  62£  lb.,  the  rest  of  the  weight  of  the  plank 
being  carried  by  the  fulcrum  (the  ground),  (b.)  The  length 
of  the  inclined  plane  is  4  times  its  height  196  lb.  -7-  4  = 
49  1b. 

2.  10  ft.  x  ft  =  30  fa—Ans. 

3.  15  lb.  x  6  =  90  lb.— Ans. 

4.  The  power  moves  40  inches  while  the  weight  moves 
i  inch.     40  -T- 1  =  160. 

1600  Kg.  -T-  160  =  10  Kg. 

5.  30  lb.  x  160  =  4800  lb. 

4800  lb.  —  480  lb.  =  4320  lb.     Or  we  may  deduct 
the  ^  from  the  30  lb.  and  say  27  lb.  x  160  =  4320  lb. 


14  [First  Principles  of  Natural  Philosophy,  p.  &£.] 

Review  Questions,  Page  94. 

1.  By  thus  raising  the  centre  of  gravity  above  the  point 
of  support,  he  may  put  the  boat  in  unstable  equilibrium. 
§§  163  (b.)  and  69. 

2.  §  144. 

7.  §  21.  (a.)  The  pupils  will  enjoy  your  reading  to 
them  this  poem  of  Shelley's. 

10.  The  momentum  of  the  "  run"  adds  its  effect  to  the 
muscular  effort  of  the  "  jump." 

11.  (a.)  The  effect  of  gravity  is  less  1000  miles  above  the 
surface  of  the  earth  than  it  is  at  the  surface  (§63).  Con- 
sequently at  that  elevation  it  would  take  a  larger  lump  to 
pull  down  the  spring  of  the  balance  as  far  as  a  pound 
would  pull  it  here.  (J.)- The  elasticity  of  the  spring 
would,  probably,  not  be  affected  by  its  greater  distance 
from  the  earth's  centre,  but  with  the  lever  balance,  the 
weight  and  counter  weight  would  be  equally  affected.  In 
one  case,  the  standard  is  constant ;  in  the  other,  it  is 
changeable. 

12.  Cohesion.     §§  7,  30. 

13.  Cohesion. 

14.  Cohesion. 

15.  See  Hand-Book  note  on  that  exercise.  P  is  at  one 
end  of  the  plank ;  W,  at  the  middle  ;  F,  at  the  other  end 
which  rests  on  the  ground. 

16.  (a.)  Adhesion,  (b.)  Grease  the  outside  of  the  jar 
at  the  part  over  which  the  water  is  poured. 

17.  10  lb.  x  {m  =  U  K>.—Ans. 

18.  §  73. 

20.  K.  E.  =  £  =  1Q°  X  1°ZXJ00°  =  6218905.47, 
2g  64.32 

the  number  of  foot-pounds. 


[First  Principlt*  of  yat'tra'  Phi  osophy,  pp.  MJ-112.]       15 

Ej-erriscs.    Pa  /r    Ht<>. 

1.  100  lb.  x  V-  X  -^P*  =  10  000  000  11). 

2.  In  the  basement,  because  the  "imaginary  column* 
will  be  higher,  i.e.,  the  head  (§  171)  will  be  greater. 

3.  The  exposed  surface  is  250  sq.  ft.  (§  158.)  The 
imaginary  column  is  5  ft.  high  and  has  a  volume  of  L250 
cu.  ft.  Such  a  volume  of  water  would  weigh  62.42  lb.  x 
1250  =  78025  lb. 

4.  6  x  8  x  4  =  192,  the  number  of  cubic  feet. 

62.42  lb.  x  192  =  11984.64  lb. 

5.  2  x  3  x  1.5  =  9,  the  number  of  cubic  meters.  Each 
cubic  meter  equals  1000  cu.  decimeters  or  liters.  (Ap- 
pendix B.)  Each  of  the  9000  liters  of  water  weighs  1 
kilogram  (for  each  liter  contains  1000  cu.  cm.,  and  each 
:u.  cm.  of  water  weighs  one  gram). 

Exercises,  Paffe  112. 

1.  In  the  valley,  because  the  pressure  will  vary  with  the 
depth  below  the  surface  of  water  in  the  reservoir. 

2.  50  lb.     §  163. 

3.  1  cu.  ft.,  which  will  weigh  62.42  lb. 

5.  Consult  biographical  dictionary  or  cyclopaedia. 

4.  It  will  displace  1  cu.  ft.  of  water  and,  therefore 
(§  162),  lose  62.42  lb.  of  its  weight. 

6.  (a.)  Its  own  weight,     (b.)  Its  own  volume. 

7.  When  its  centre  of  gravity  is  below  its  centre  of 
"buoyancy.  It  may  be  necessary  for  the  boat  to  carry  ballast 
to  keep  it  there. 

8.  Because,  while  it  is  in  the  water,  it  is  buoyed  up  with 
a  force  equal  to  the  weight  of  its  own  volume  of  water ; 
after  that,  the  buoyant  effect  is  only  the  weight  of  its  own 
volume  of  air. 

!».  Because  you  displace  a  volume  of  water  that  weighs 
nearly  as  much  as  you  do.  Thus,  you  are  nearly  lifted 
from  the  ground. 


16       [First  Principles  of  Natural  Philosophy,  pp.  116-121.] 

Exercises,  Page  116. 

1.  It  loses  50  lb.  in  water.  Its  volume  of  water  weighs 
50  lb.  The  body  is  three  times  as  heavy  as  its  own  volume 
of  water.     This  means  that  its  specific  gravity  is  3. 

a  W  150  150 

*■  ^  ==  WW  =  150^100  =  To"  f  d'~Ans- 

2.  75  oz.  —  60  oz.  =  15  oz.—  Ans. 

3.  No ;  it  will  float.     Try  it  before  the  class  if  you  can. 

4.  It  will  lose  1.8  times  as  much  weight  in  the  acid. 

5.  In  fresh  water.  The  buoyancy  of  the  salt  water  will 
be  the  greater. 

6.  It  is  well  known  to  be  easier  to  swim  or  float  in  sea 
water  than  it  is  in  fresh  water. 

7.  The  volume  of  the  overflowing  water  was  equal  to 
the  volume  of  the  brass.     41.9  oz.  -f-  5  oz.  =  8.38. 

8.  The  bottle  will  hold  (1000  cu.  cm.)  1000  grams  of 
water.  The  same  volume  of  water  weighs  (800  grams  -=- 
1000  grams  =  )  0.8  as  much.  That  is,  the  sp.  gr.  of  alco- 
hol is  0.8.  Eemember  that  the  weight  of  an  equal  volume 
of  water  is  always  the  divisor. 

Mevietv  Questions,  Page  121. 

1.  §  146. 

2.  §  152. 

3.  §  148. 

4.  §§  150,  111. 

5.  Solids  have  permanency  of  form ;  liquids  have  not. 
Liquids  have  freedom  of  molecular  motion  ;  solids  have 
not. 

6.  One  second.     §  86. 

7.  The  nutcracker  is  a  double  lever  of  the  second  class 
(§  109).  F  is  at  the  hinged  end  ;  the  resistance  of  the 
nut  is  W;  P  is  at  the  hand. 

9.  In  no  direction  ;  they  transmit  pressure  equally  in 
all  directions. 


[First  Principles  of  Natural  Philosophy,  pp.  1S1-12S.]       17 

10.   §  147. 

12.  The  lev  is  an  abstract  number.  It  simply  means 
ten  times  as  heavy  as  water.  All  multipliers  are  abstract 
numbers. 

16.  The  centre  of  gravity  is  thus  brought  lower.  As 
shown  in  the  figure,  the  apparatus  is  still  in  unstable 
equilibrium.  The  knives  might  be  brought  low  enough 
to  bring  the  centre  of  gravity  below  the  point  of  support, 
and  thus  put  the  apparatus  in  stable  equilibrium  (§§  73,  66). 

Exercises,  Page  128. 

1.  Because  the  upward  atmospheric  pressure  is  as  great. 

2.  Water  would  rush  in.  The  tension  of  the  air  in  the 
bottle  would  be  only  that  of  the  atmosphere  at  the  mount- 
ain top,  and  this  is  less  than  atmospheric  pressure  at  the 
sea  level. 

3.  The  exposed  surface  is  1728  sq.  in.  15  lb.  x  1728  = 
25920  lb. 

•    4.  The  exposed  surface  is  (100  x  200  =  )  20000  sq.  cm. 
The  pressure  is  a  kilogram  for  each  sq.  cm.    Arts.,  20000  Kg. 

5.  To  prevent  the  downward  pressure  of  the  atmosphere 
on  the  top  of  the  mercury  column. 

6.  To  permit  the  atmosphere  to  act  upon  the  bottom  of 
the  mercury  column  and  thus  to  support  it. 

7.  The  mercury  is  13.6  times  as  heavy  as  water. 

28  in.  x  16.6  =  380.8  in.  =  31  ft,  8$  in. 

8.  The  boiler  was  subjected  to  an  internal  pressure  of 
150  lb.  per  sq.  in.  This  test  might  have  been  hot  or  cold ; 
steam  may  have  been  generated  in  the  boiler  until  the 
steam  gauge  recorded  a  pressure  of  150  lb.,  or  the  boiler 
may  have  been  filled  with  water  and  hydrostatic  pressure 
applied  (§  150).  The  cold  test  is  considered  the  more 
severe. 


18      [First  Principles  of  Natural  Philosophy,  pp.  137,  138.] 

Exercises ,  Page  137, 

1.  The  cube  has  six  faces.     Its  total  surface  is  6  sq.  in. 

15  lb.  x  6  =  90  lb.—  Ans. 

2.  28  ft.  =  336  in.      336  in.  -f-  13.6  =  24|f  m.—A?is. 

3.  By  placing  the  pump  within  28  ft.  of  the  surface  of 
the  water  and  extending  the  spout  (Fig.  70)  to  the  top  of 
the  well.  The  cylinder  of  the  pump  may  be  a  tube  ex- 
tending to  the  top  of  the  well,  the  piston  rod  running 
down  the  inside  of  such  long  cylinder. 

4.  The  tension  of  the  air,  when  you  blow  in  at  /,  lifts 
the  water  to  h  and  fills  the  tube.  The  tube  then  consti- 
tutes a  siphon  and  continues  to  deliver  water  into  g.  The 
rising  of  the  water  in  g  reduces  the  air  space  and  thus 
increases  the  tension  of  the  air  in  g,  i  and  a.  This  in- 
creased pressure  exerted  by  the  air  on  the  surface  of  the 
water  in  a  is  transmitted  to  the  water  contained  in  a  and 
forces  it  out  in  a  jet  at  n. 

6.  Atmospheric  pressure. 

7.  1728  cu.  in. -5-  8  =  216  cu.  in. 

Review  Questions,  Page  138. 

1.  (a.)  The  bottle  contains  air.  §  19.  (b.)  The  air  is 
compressed  by  the  liquid  pressure. 

2.  (a.)  §§  22,  49.  (b.)  Chiefly,  the  friction  of  the  water 
against  the  sides  of  the  hull. 

3.  Because  of  the  continued  action  of  gravity. 

5.  The  Third  Law  of  Motion.  The  particles  that  first 
hit  the  target  are  stopped,  but  other  particles  press  forward, 
overcoming  the  force  of  cohesion  until  they  are  stopped  by 
the  target. 

6.  Because  of  the  continued  action  of  gravity,  the  force 
that  produces  the  velocity. 

7.  Much  of  it  is  stored  up  in  the  pyramids  as  potential 
energy. 


[First  Principles  of  Natural  Philosophy,  pp.  /::>-?o5.]       19 

8.  A  double  lever  of  the  first  class.  P  is  at  the  hand; 
F,  at  the  rivet ;    W,  at  the  cord. 

a  3  iG7. 

10.  Once  a  second.    §  87. 
12.  §§  79  (3),  82. 
14.  §  161. 

Exp.  9S.  The  clapper  is  polarized,  attracted,  charged, 
repelled,  discharged,  polarized  again,  etc. 

Exp.  97.  After  the  leaf  is  charged  by  touching  the 
rod,  the  similar  charges  repel  each  other  (§  214). 

Exp.  98.  The  pupil  being  charged  by  conduction, 
polarises  and  attracts  the  yard-stick  (g  225). 

Exp.  99.  When  the  cover  is  lifted  from  the  plate,  the 
bound  electricity  is  set  free  and  then  similarly  charges 
and  repels  the  paper  bits.     See  Elem.  Nat.  Phil,  §  338  (6-). 

Exp.  103.  See  §  240.  The  repulsion  of  the  air  par- 
ticles for  the  similarly  charged  arms  of  the  whirl  produces 
the  motion.  This  is  not  a  case  of  the  mere  reaction  of  the 
repelled  air  particles.     See  §  54. 

Exercises,  Paye  179. 

1.  Because  they  produce  opposite  effects  when  presented 
to  a  third  charged  body.  See  §  211.  Also  Eton.  Nat. 
Phil,  §  322  and  Exp.  22,  p.  194. 

3.  Electroscope. 

4.  See  §  214. 

5.  To  prevent  the  condensation  of  atmospheric  moisture. 

6.  (b.)  §  224.     (c.)  Opposite. 

Exercises,    I'at/e  205. 

1.  The  greater  action  is  upon  the  zinc.  See  §  249  aud 
Fig.  102. 

2.  (a.)  By  making  the  plates  larger ;  by  bringing  them 
nearer  each  other ;  by  preventing,  by  mechanical  or  chem- 


20         [First  Principles  of  Natural  Philosophy,  p.  205.\ 

ical  means,  the  accumulation  of  hydrogen  upon  tbe 
negative  plate.  The  internal  resistance  of  a  battery  may 
be  lessened  by  joining  the  cells  parallel,  (b.)  By  in- 
creasing the  E.  M.  F.,  or  by  reducing  the  circuit  resist- 
ance.    §§  252,  265,  266. 

3.  See  §  254. 

4.  3.02  :  22.65  =  18.12  :  135.9.     Ans.,  135.9  yd. 

6.  §§  273,  260.  1.079  volts  is  less  than  the  E.  M.  F.  of 
the  ions  (1.45  volts),  while  2.158  volts  is  greater. 

7.  Assume  any  number  of  volts,  as  1  volt,  as  the  inter- 
nal resistance  of  the  Grove  cell,  and  find  the  current 
strength  of  the  two  cells  for  comparison. 

W        1  73 
C  =  -=  =  ~~ 'Ht  1.73,    the    number    of    amperes 

with  Grove  cell. 

Tjl  -t      f\Q 

O  =  -„■  =  -V-  =  0.216,   the   number  of    amperes 

with  Daniell  cell. 

1.73  -T-  0.216  =  8  + 

To  make  the  solution  more  general,  call  the  internal 
resistance  of  the  Grove  cell,  a  ohms. 

1.73 

Grove  current  =  — — 
a 

Daniell     "        =  ^~ 
5a 

1.73       1.08       1.73         5a       „  „.       ., . 

'-  -z —  = X  =-x^.     By  cancelling  the  fao* 

a  5a  a         1.08        J  b 

tor,  a,  in  numerator  and  denominator,  we  have  : 

1.73  5      _  8.65  _  Q 

1      X  1.08  -  1.08  "      +* 


[First  Principles  of  Natural  Philosophy,  p.  205.]  'i\ 

8.  (a.)  The  E.  M.  F.  will  be  6  times  that  of  a  single  cell. 
(b.)  The  internal  resistance  will  be  J  that  of  a  single 
cell. 

ET  200 

9-  («•>  C  =  R  =  25  +  1000  =  °-195  +  -     (In  8erieS-) 
W  C=  1  =  0.0025 +  1000=0-°019  +  -    (AbrcaSt-) 
10"  «  C  =  I  =  0.0025  +  0.001  7  571A    (AbreaSt) 

<»•)  c  =  i  =  sstSm  =  m  F**^ 

11.  Single  celL     0  =  §  =  -^^  =  7.96a 

XT  -i  nrv 

50  cells.     C=_=___  =  7.999. 

With  a  small  external  resistance,  there  is  but  little  gain 
from  joining  cells  in  series. 

Joining  more  cells  in  series  will  multiply  numerator 
and  denominator  by  the  same  number  and  will  not  change 
the  quotient,  which  will  continue  to  indicate  a  current  of 
8  amperes. 


22      [First  Principles  of  Natural  Philosophy,  pp.  226-243.'] 

Exercises,  Page  226. 

2.  No ;  you  have  two  magnets. 

6.  It  can  not  be  done. 

7.  Make  the  experiment. 

8.  Put  the  magnet  in  a  hollow  iron  sphere. 

9.  See  Mem.  Nat.  Phil,  §  437. 

10.  See  Exp.  133. 

12.  Make  the  experiment. 

Exercises,  Page  242. 

1.  Use  the  power  to  operate  the  dynamo,  extend  the 
line  wire  to  his  residence  and  use  arc  or  incandescence 
lamps,  or  both. 

2.  §  308. 

3.  (a.)  The  electric  light,  (b.)  The  3468  cu.  ft.  of  gas 
per  hour  would  cost  $6,936,  showing  a  saving  of  $4.73 
each  hour,     (c.)  $14208. 

Review  Questions,  Page  243. 

2.  Second  class. 

3.  Wedge. 

4.  Weight,  height,  time. 

5.  By  sucking  at  b,  a  partial  vacuum  is  formed  in  /. 
Atmospheric  pressure  on  the  surface  of  the  water  in  a, 
forces  the  liquid  up  the  tube  and  forms  the  jet.  As  b  is 
lower  than  the  surface  of  the  water  in  a,  gravity  draws 
the  water  downward  through  it,  maintaining  a  partial 
vacuum  in  the  closed  flask,  into  which  vacuum  water  con- 
tinues  to  be  forced.  In  fact,  the  apparatus  is  a  siphon 
with  an  enlarged  portion  at  its  highest  point. 

7.  Make  the  experiment. 

8.  The  lightning  flash. 

9.  Impenetrability. 

10.  The  tendency  of  the  molecules  to  cling  together  in 
one  case,  or  to  separate  in  the  other.     Both  are  fluids. 


[First  Princip  'iral  Philosophy,  p.  24S.]  28 

12    C-  £  -  839 -  ^-9  -  10 

i?  ""  (4.56  x  lg)  +  10.54  +  0.4  ~~  8.39  " 

Ans.9  10  amperes. 

13.  Neither  ;  they  are  developed  simultaneously. 

14.  See  §  231. 

16.  (a.)  v  =  gt  =  32.16  ft.  x  5  =  160.8  ft.—  Ans. 
\b.)  S  =  W2  =  16-08  ft-  x  25  =  402  ft.— Am. 

17.  See  Exp.  111.  If  convenient,  use  fine  platinum 
wire  instead  of  the  iron  wire. 

18-  c=  i  =  (WxTO)+io= is=0-39-^- 

19.  Make  the  experiment. 

20.  Remember  that  the  glass  rod  was  positively  charged. 
If  you  noticed  attraction,  the  paper  must  have  been  neg- 
atively charged.  If  you  noticed  repulsion,  the  paper  was 
positively  charged. 

21.  It  is  the  difference  between  conductors  and  non- 
conductors. In  other  words,  it  is  a  matter  of  resistance. 
The  brass  carried  the  electricity,  as  fast  as  it  was  developed, 
to  the  hand  and  allowed  it  to  escape  through  the  body. 
The  resistance  of  the  sealing-wax  prevented  such  an 
escape. 

22.  s  =  \g  (21  —  t).     See  §  82. 

337.68  =  16.08  (2t  —  1).     Dividing  by  16.08: 

21  =  2t  —  1.     Adding  1  to  each  side  of  equation. 

22  =  2/.    .-.  11  =  t.    Ans.,  11  sec. 

23.  The  imaginary  column  of  water  (§  157)  contains  : 

(42  x  6  =)  252  cu.  in.,  or  ^ff  cu.  ft. 

62.42  lb.  x  tWj  =  9.1  lb.— Ans. 
317.  The  teacher  is  referred   to   TyndalPs  Lectures 
on   "Sound";  Helmholtz's   "Sensations  of  Tone"  and 
Mayer's  "  Sound,"  mentioned  in  §  320,  a. 


24       [First  Principles  of  Natural  Philosophy,  pp.  258-279.] 
Exercises,  Page  258. 


2.  The  temperature  is  0°C.    §  325.    Ans.,  1090  ft 

3.  §  321.     1280  ft.  -f-  256  =  5  it.— Ans. 

4.  1090  ft.  -f-  218  =  5  ft.— Ans. 

5.  §  325.    332  meters  -f-  1  meter  =  332.     §  321. 

Ans.,  332  vibrations  per  second. 

6.  The  temperature  is  20  centigrade  degrees  above 
freezing. 

§326.   2ft.x20=40ft.   1090 ft. +  40 ft. =1130 ft.— Ans. 

7.  1126  ft.  -  1090  ft.  =  36  ft. 

36  ft.  -7-  2  ft.  =18,  the  number  of  centigrade  degrees 
above  freezing,  or  above  the  centigrade  zero.     Ans.,  18°C. 
36  ft.  -T-  1.12  ft.  =  32.14,  the  number  of  Fahrenheit 
degrees  above  freezing  or  above  32°F. 

32  +  32.14  =  64.14.      Ans.,  64.14°F. 
The  increments  mentioned  in  §  326  are  only  approxima- 
tions.    The   temperature,   18°C,  is  really  equivalent  to 
64.4°F.,  instead  of  64.14°F. 

Exercises,  Page  279. 

1.  (a.)  The  first.     (J.)  The  second. 

2.  1120  ft.  -^  280  =  4  ft— Ans. 

4.  254  or  258.     §  345. 

5.  Vibratory. 

6.  In  the  first,  the  particles  vibrate  in  the  line  of  propa- 
gation of  the  motion,  as  in  a  sound  wave.  In  the  second, 
the  particles  vibrate  across  the  line  of  propagation,  as  in  a 
water  wave. 

7.  Zero.     §  324. 

8.  The  rapidity  of  vibration  of  the  sounding  body. 


[  First  Principles  of  Natural  Philosophy,  p.  280.] 
1!<  ri<  tr  Que#tioti8,  Page  280. 


25 


1.  (a.)  By  changing  its  tension  by  means  of  the  pegs, 
or  by  changing  its  length  by  fingering. 

(b.)  Both  electricities  are  in  the  body,  but  they  are  sep- 
;u;ik(l,  one  being  attracted  and  the  other  being  repelled 
by  the  charge  of  the  polarizing  body. 

2.  Imagine  the  weight  of  the  door  concentrated  at  its 
centre  of  gravity.  Fulcrum,  at  the  hinges;  Hr,  at  middle 
of  door;  P,  between   Hand  F;  3d  class. 

3.  Place  c  in  the  acid ;  close  the  opening  in  b  ;  suck  at 
a  until  the  acid  runs  into  b  ;  remove  the  stopper  from  b. 

4.  Transverse  waves  moving  outward  in  concentric 
circles  from  the  centre  of  disturbance. 

5.  Longitudinal  waves  moving  outward  in  concentric 
spherical  shells  from  the  bell  as  a  centre. 

9.  §  167. 

10.  §  272. 

11.  §  321. 

12.  (a.)  10900  ft,  or  3320  m.  (b.)  That  I  may  know 
the  velocity.     §  326. 

13.  Electro-magnet. 


26       [First  Principles  of  Natural  Philosophy,  pp.  288-296.] 

Exercises,  Page  2 88. 

1.  15°  x  1  =  27°     27  +  32  ==  59.     Ans.,  59°  F. 

2.  59°  —  32  =  27.     27  x  f  =  15.    Ans.,  15°  C. 

3.  273  +  15  =  288.  Ans.,  288°  C.  (absolute).  That 
the  temperature  in  question  is  288  centigrade  degrees 
warmer  than  that  at  which  there  are  no  molecular  motions 
constituting  heat. 

4.  By  rubbing  a  brass  button  on  the  floor,  or  by  any 
other  means  of  producing  friction. 

5.  §§363,364. 

E&ereises,  Page  296. 

1.  At  the  same  temperature,  115°  C.     §  368  (1). 

2.  §§  370,  371. 

3.  By  heating  it  in  a  closed  vessel  so  that  the  pressure 
of  its  own  vapor  is  exerted  upon  the  liquid.  E.  g. ,  the 
water  in  a  steam  boiler  under  a  pressure  of  10  atmos- 
pheres is  356.6°  F.,  instead  of  212°  F. 

4.  See  Elem.  Nat.  Phil,  §§  571,  572. 

5.  Steam  is  invisible. 

6.  §  374. 

7.  By  distillation.  Most  naval  vessels  and  ocean  steam- 
ers are  provided  with  distillation  apparatus  for  use  in 
emergency. 

8.  0°  C,  or  32°  F.     §  368  (2). 

9.  (a.)  About  1700  cu.  ft.    (b.)  About  850  cu.  ft. 


[First  Principles  of  Natural  PKUowphy,  pp.  Jo;-        j        J? 

I.i rrrisrs.     I'tlt/r    .iO}. 

1.  §  382. 

2.  Yes  ;  by  the  withdrawal  of  heat  to  do  the  work  of 
vaporizing  the  liquids  on  the  tongue. 

3.  To  cool  it  by  the  abstraction  of  the  heat  used  in  the 
work  of  vaporization. 

4.  §  384.     144  x  3  =  432. 

5.  The  increase  of  temperature  is  212  —  32  =  180. 

'80x3  =  540. 

6.  §  385.      537   x  3  =  1611,    the   number  of    lesser 
calories. 

7.  To  melt  the  ice  (144  x  3  =)  432  units. 

To  warm   the   water  from   32°  to  212° 

(180  x3=)  '     540     " 

To    vaporize     the    boiling    hot     water 

(967x3=)  2901     " 

Total,  3873     " 

8.  1  kilogram  =  1000  grams. 

To  warm  the  ice  to  0°  C,  5000  lesser  calories, 

To  melt  the  ice,  80000     " 

To  heat  the  water  from  0°  0.  to 

15°  C,  15000     "  " 

Total,  100000     " 

Or  100  calories.     See  Elem.  Nat.  Phil,  §  579,  a. 

722,000  lesser  calories  would  convert  the  ice  into  steam. 

Exercises,  Page  316, 

1.  Because  a  moist  atmosphere  is  a  better  conductor  of 
heat  than  a  dry  one. 

2.  Because  the  bodily  heat  is  carried  away  in  part  by 
convection. 


28       {First  Principles  of  Natural  Philosophy,  pp.  316-334.] 

3.  Because  some  are  better  conductors  than  others.  In 
a  cold  room,  the  good  conductors  carry  heat  from  the 
person  with  rapidity  and  thus  give  us  the  sensation  of 
cold. 

4.  (a.)  A  non-conductor,     (b.)  A  non-conductor. 

5.  By  conduction. 

6.  For  radiation.     §  404. 

Exercises,  Page  324, 

1.  424  m.,  or  1390  ft.    §  413. 

2.  The  given  amount  of  heat  will  do  the  same  amount 
of  work  as  in  the  former  case  and  lift  twice  the  weight 
just  half  as  high.     §  95. 

3.  212  ra.,  or  695  ft. 

4.  424  m.,  or  1390  ft. 

5.  It  will  lift  its  own  weight  (10  lb.)  424m.,  or  1390  ft, 
or  half  that  weight  twice  as  high. 

6.  It  will  lift  its  own  weight  424  m.,  or  1390  ft.,  or 
twice  its  weight  to  half  that  height.  Ans.,  212  m,,  or 
695  ft. 

7.  One  heat  unit  (pound-Fahrenheit). 

8.  Two  heat  units  (pound-Fahrenheit). 

9.  One  unit  for  each  gram  so  raised.    Ans.,  1000  units. 

10.  This  work  is  twice  as  great  as  that  mentioned  in  the 
last  Exercise.     It  will,  therefore,  take  twice  as  much  heat. 

11.  We  have  placed  at  our  disposal  34462  heat  units 
(gram-centigrade).  §  411,  a.  Each  gram  of  water  will 
require  100  units.  34462  -f-  100  =  344.62,  the  number 
of  grams. 

12.  We  now  have  8080  units.     8080  +  100  =  80.8. 

14.  Nearly  1£  times  as  much ;  -^^  times  as  much. 
§  411,  a. 

15.  Heat  can,  by  being  converted  into  some  other  form 
of  energy.     Energy  cannot. 


[First  Principles  of  Saturn!  Philosophy,  p.  325]  29 

Retrteu)  <>m  stinns.  I'atjr  :;?.>. 

1.  Weight,  length  and  tension. 

2.  (a.)  Yes.     (b.)  No.     §  894. 

3.  Perhaps  a  little  mercurial  vapor.  Otherwise  it  should 
fje  a  vacuum. 

4.  Amplitude  of  vibration.     §  330. 

5.  To  provide  for  expansion  in  warm  weather. 

G.  Because  the  alcohol  that  fills  the  gallon  measure  iu 
winter  expands  with  summer  heat  so  that  only  a  part  of  it 
will  go  into  the  same  measure.  The  measure  will  hold  a 
greater  number  of  alcohol  molecules  in  January  than  it 
will  in  August.  The  gallon  measure  is  supposed  to  have 
a  capacity  of  a  gallon,  or  231  cu.  in.  in  each  case. 

7.  No.  There  is  no  atmospheric  pressure  to  lift  the 
liquid  against  the  force  of  gravity. 

8.  Very  little,  for  want  of  sufficient  pressure  on  the 
surface  of  the  water  in  the  cistern  when  a  little  is  removed. 
The  water  would  give  its  vapor  to  the  space  thus  made 
vacant,  but  its  tension  would  not  be  sufficient  to  lift  the 
water  to  any  considerable  height. 

9.  Yes  ;  on  account  of  the  tension  of  the  confined  air. 

10.  Close  a  bottle  full  of  water  with  a  cork  perforated 
by  a  glass  tube  dipping  into  the  water.  Try  to  suck  out 
■ome  of  the  water  and  you  will  fail.  Repeat  the  experi- 
ment with  a  bottle  half  full  of  water  and  you  will  succeed. 

11.  A  windy  day.     Loss  of  bodily  heat  by  convection. 

12.  Much  greater.     §  390. 

13.  No.     §  363. 

U.  See  answer  (in  this  Hand-Book)  to  Ex.  3,  p.  296. 

15.  Solids  and  liquids  have  different  rates  of  expansion. 
A.11  gases  expand  at  practically  the  same  rate.  See  Elem. 
Nat.  Phil,  %  557. 

16.  Third  class.  F  is  at  the  bend  of  the  tongs ;  P  is 
where  the  fingers  are  applied;  W  is  at  the  lump  held  in 
the  tongs. 


80  [First  Principles  of  Natural  Philosophy,  p.  325.'] 

17.  Heat  is  withdrawn  from  the  body  for  vaporization. 

18.  50°  C. 

19.  (a.)  When  drops  fall  from  c,  the  space  occupied  by 
the  quantity  of  air  confined  iu  the  bottle  is  increased  ; 
this  lessens  the  tension  of  the  air  thus  confined,  soon 
bringing  it  so  low  that  atmospheric  pressure  at  a  forces  air 
inward,  overcoming  the  pressure  of  the  water  at  the  lower 
end  of  the  tube.  This  pressure  of  the  water  is  due  to  its 
own  gravity  and  to  the  pressure  exerted  upon  its  surface 
by  the  confined  air.  (b.)  When  air  can  no  longer  enter  at 
a,  the  tension  0  c  the  confined  air  diminishes  with  the  fall- 
ing of  each  drop  at  c  and  the  consequent  increase  of  the 
air  space  in  the  bottle.  Soon  this  tension  becomes  so 
small  that  it  and  the  weight  of  the  water  are  together  less 
than  the  upward  atmospheric  pressure  at  c. 

20.  Sound  waves.  The  vibrations  of  the  ball  are  longi- 
tudinal. 

21.  (33  x  1.8)  +  32  =  91.4.     Ans.,  91.4°  F. 

1.8  =  |.     §  360. 

22.  By  the  boiling  away,  the  lower  end  of  the  tube  is  un- 
covered. Air  then  enters  the  bottle.  Water  from  the 
bottle  raises  the  liquid  surface  in  the  basin  until  the  end 
of  the  tube  is  sealed  against  the  further  admission  of  air. 
The  water  will  be  kept  at  that  level  as  long  as  there  is  any 
water  in  the  bottle. 

23.  See  §  189.  24.   See  §  332. 
25.  See  §  363.  26.   See  §  366. 

27.  (a.)  The  atmosphere,  (b.)  The  luminiferous  ether. 
§396. 

28.  See  §  153. 

29.  See  §  272. 

30.  See  §  82.  v  =  gt  +  20  =  (9.81  x  4)  +  20  == 
39.24  +  20  =  59.24.     Am.,  59.24  m. 

31.  The  First  Law  of  Motion.     §§  51,  52. 

32.  See  §  326. 

33.  See  §  11,  a. 


[First  Principles  of  Natural  Philosophy,  pp.  335-346.]     31 

EjCirrisrs,     I'tHJC    3M< 

1.  Less.  Water  waves  are  transversal  like  luminous 
waves ;  sound  waves  are  longitudinal  unlike  luminous 
waves. 

2.  §  420. 

3.  A  collection  of  rays  emitted  by  the  sun.  Owing  to 
the  great  distance  of  the  sun,  the  rays  that  come  to  any 
place  on  the  earth  are  practically  parallel.     §  424. 

4.  See  §  426. 

5.  Eight  minutes  and  eighteen  seconds.     §  427,  a. 

6.  It  would  be  one  fourth  as  intense.     §  428. 

7.  (a.)  Neither,  (b.)  The  more  distant  one  has  four 
times  the  luminous  power  of  the  other. 

8.  See§  421, 

12  inches  =  1  foot.  The  wall  is  100  times  as  far 
away  as  the  screen.  Each  side  of  the  shadow  will  be  100 
times  the  length  of  one  side  of  the  screen,  i.  e.,  300  inches. 
Therefore,  the  area  of  the  shadow  will  be  (1  sq.  in.  x  300 
X  300  =)  90000  sq.  in.     See  Exp.  210  and  §  428. 

10.  The  lamp  gives  an  equal  illumination  at  three  times 
ihe  distance.     32  =  9.     The  lamp  is  of  9  candle  power. 

Il.nrciscs,    i'ttf/c  340. 

1.  Locate  the  three  points  on  the  paper  and  letter  them. 
Draw  the  lines,  A  C  and  B  C.  Bisect  the  angle,  A  C  B, 
by  the  line,  CD.  Through  6',  draw  the  line,  m  n,  perpen- 
dicular to  CD.  This  line,  m  n,  indicates  the  position  of 
tlie  mirror.  The  angle,  A  C  D,  is  the  angle  of  incidence. 
Yh?  angle,  B  CD,  is  the  angle  of  reflection.  They  were 
<  (jual  in  accordance  with  §  431. 

.'  Because  the  spot  transmits  more  light  to  the  eye  than 
does  the  rest  of  the  piper. 

3.  Because,  as  the  spot  transmits  more  light  than  the 
rest  of  the  paper,  it  reflects  less  to  the  eye. 

4.  See  §  440.  5.  See  §  434.  6.  See  §  434. 


32  [First  Principles  of  Natural  Philosophy,  p.  364.] 

Exercises,  Page  364. 

2.  (b.)  See  §  542,  a. 

4.  See  the  secondary  axes,  A  0 a  and  B  Ob,  m  Fig. 220 

5.  See  §  456. 

C.  A  straight  line  passing  through  the  centre  of  a  circle. 

7.  Draw  the  chord  of  a  circle  (other  than  a  diameter)  to 
i-3present  the  path  of  the  wave  through  the  glass.  From 
the  ends  of  this  chord,  draw  straight  lines  representing 
the  paths  of  the  wave  before  and  after  refraction.  These 
lines  gradually  approach  the  prolongations  of  a  diameter 
parallel  to  the  chord  first  drawn. 

8.  See  the  line,  L  a  b  c,  in  Fig.  214. 

9.  Draw  an  isosceles,  right-angled  triangle.  From  any 
point  on  the  hypothenuse,  draw  lines  cutting  the  other 
two  sides  perpendicularly.  Prolong  these  lines.  These 
two  lines  form  a  right  angle  at  the  hypothenuse  and  rep- 
resent the  path  of  the  ray.  See  §  444  (1).  The  ray  is 
reflected  (§  445)  at  the  hypothenuse  because  the  incident 
angle  (45°)  exceeds  the  critical  angle  for  glass.  See  Ehm. 
Nat.  Phil,  §  682. 

10.  (a.)  See  Fig.  219  (1).  (b.)  See  Fig.  218  (2). 
(c.)  The  rays  will  converge  on  the  other  side  of  the 
lens,  on  the  principal  axis,  between  the  principal  and 
secondary  foci.     See  Fig.  218  (1).     (d.)  See  Fig.  219  (2). 


[First  Principles  of  Natural  Philosophy,  p.  S72.]  33 

Exercises,  Page  372. 

1.  The  first  is  an  effect  of  reflection  (§  432)  ;  the  second 
ii  an  effect  of  refraction  (§  468), 

2.  When  the  body  sends  red  rays  to  the  eye. 

3.  Violet,  indigo,  blue,  green,  yellow,  orange,  red.    §  462. 

4.  Pitch,  both  being  determined  by  rate  of  vibration  or 
wave  length. 

5.  Because  the  glass  transmits  green  rays  and  absorbs 
or  reflects  the  others. 

6.  No.     Color  is  a  property  of  light  and  not  of  matter. 

7.  (a.)  One  second. 

(b.)  See  §467.  39000  waves  per  inch. 

39000  x  12      "       "  foot. 
39000  x  12  x  5280      "       "  mile. 
39000  x  12  x  5280  x  186000  =  the  number  of  wavea 

— Am. 
(c.)  39000  x  12  x  5280  x  186000  =  the  number  of  waves. 

A  71S. 

8.  (a.)  Yes.  (b.)  Because  it  is  visible.  See  §  425,  a. 
(c.)  Red.  See  §  465.  (d.)  They  are  absorbed  and  warm 
the  ribbon. 

9.  Converging  lenses  are  represented  in  Fig.  215  (1), 
(2)  and  (3).  They  render  parallel  incident  rays,  converg- 
ing ;  make  converging  rays  more  converging,  and  diverg- 
ing rays  they  make  less  diverging.  Diverging  lenses  are 
represented  in  Fig.  215  (4),  (5)  and  (6).  They  render 
parallel  incident  rays  diverging;  make  diverging  rays 
more  diverging,  and  converging  rays  they  make  less 
converging. 

10.  Refraction^  reflection,  dispersion. 


34  [First  Principles  of  Natural  Philosophy,  p.  384.] 

General  Review,  Page  384, 

Suggestion. — Use  the  index  freely. 

5.  Multiply  the  velocity  of  sound  at  the  observed  tem- 
perature (§§  325,  326)  by  the  number  of  seconds  that 
intervene  between  seeing  and  hearing  in  cases  like  those 
mentioned  in  §  325. 

7.  In  passing  through  the  earth's  atmosphere,  they  are 
continually  refracted  in  accordance  with  §  444  (2),  for  the 
atmosphere  is  continually  increasing  in  density  from  its 
upper  to  its  lower  limit.  As  the  ray  is  continually  re- 
fracted, it  changes  its  direction  at  every  point,  i.  e.,  it  is 
curved. 

11.  The  reflected,  as  well  as  the  incident,  rays  will  be 
parallel. 

12.  No.     §  444  (1). 

13.  See  Fig.  207.  If  the  eye  be  directly  above  the 
stick,  it  will  not  appear  bent  at  the  surface  of  the  water, 
because  the  rays  that  enter  the  eye  and  picture  the  stick 
upon  the  retina  are  not  refracted  in  passing  from  one 
medium  to  another.     §  444  (1). 

14.  See  §  457. 

15.  On  account  of  expansion  by  the  summer  heat. 

16.  See  §  8,  c,  and  §  24,  b. 

18.  See  §  384. 

19.  Yes.     §  53. 

20.  The  lamp  is  4  times  as  far  away.  Its  illuminating 
power  is  (42  =)  16  times  that  of  the  candle.     §  428. 

21.  No.     See  Fig.  224. 

22.  A  pound  of  ice.  Every  one  knows  that  ice  will  float 
on  water,  t.  e.,  that  it  is  lighter  than  water. 

23.  See  Exp.  180. 

25.  It  changes  the  intermolecular  distances ;  not  molec- 
ular sizes.  » 
29.  See  §  82.     S  =  igt2  =  32.16  ft.  x  10*  =  3216  ft— 

Ans. 


[Ftr*t  Principles  of  Natural  Philosophy,  pp.  J84-391.]       35 

30.  Fluid. 

31.  See  §  108. 
1  •.'.  In  no  way. 

39.  See  Mem.  Nat.  Phil,  §  301. 

42.  See  §§  363,  364,  394,  and  Epxs.  199,  200. 

47.  So  that  the  external  and  internal  resistances  shall  be 
equal  In  other  words,  it  depends  on  the  work  to  be 
done.     §  267. 

48.  See  §  425,  a. 

Exercises,  Page  391. 

1.  A  kilogram,  or  1000  grams. 

2.  1.8  kilogram,  or  1800  grams. 

3.  1250  cu.  cm.  of  water  weighs  1250  grams.  That 
quantity  of  alcohol  will  weigh  1250  g.  x  .8  =  1000  g.,  or 
1  Kg. 

4.  One  quarter. 

5.  A  cu.  dm.  is  a  liter,  or  1000  cu.  cm.,  and  weighs 
1000  g.,  or  1  Kg. 

6.  1  /.  of  water  weighs  1000  g ;  1  dl,  therefore,  weighs 
0.1  as  much,  or  100  g  =  1  Hg. 

Note. — The  denomination,  bektograin,  is  not  often  used.  Rather 
say  100  g. 


ELEMENTS 

OF 

NATURAL   PHILOSOPHY. 


CHAPTER  I. 

|?P"  The  numeral*  at  the  left  hand  side  of  the  page  refer  to  para* 
graphs  in  the  text -book. 

Introductory. — "  The  ultimate  basis  of  all  our  knowledge  is 
experience.  When  a  natural  phenomenon  arrests  our  attention,  we 
call  the  result  an  observation.  Simple  observations  of  natural 
phenomena  seldom  lead  to  such  complete  knowledge  as  will  suffice 
for  a  full  understanding  of  them.  An  observation  is  the  more  com- 
plete, the  more  fully  we  apprehend  the  attending  circumstances. 
We  are,  generally,  not  certain  that  all  the  circumstances  that  we 
note  are  conditions  on  which  the  phenomenon  in  a  given  case 
depends.  In  such  cases,  we  modify  or  suppress  one  of  the  circum- 
stances and  observe  the  effect  on  the  phenomenon.  If  we  find  a 
corres|K>nding  modification  or  failure  with  respect  to  the  phenom- 
enon, we  conclude  that  the  circumstance,  so  modified,  is  a  condition. 
We  may  proceed  in  the  same  way  with  each  of  the  remaining  cir- 
cumstances; leaving  all  unchanged  except  the  single  one  purposely 
modified,  at  each  trial,  always  observing  the  effect  of  the  modifica- 
tion. We  thus  determine  the  conditions  on  which  the  phenomenon 
depends.  In  other  words,  we  bring  kxpkkimknt  to  our  aid  in  dis- 
tinguishing between  the  real  conditions  on  which  the  phenomenon 
dependl  and  the  merely  accidental  circumstances  that  may  attend  it. 

"  But  this  is  not  the  only  use  of  experiment.  By  its  aid  we  may 
frequently  modify  some  of  the  conditions,  known  to  be  conditions, 
in  such  ways  that  the  phenomenon  is  not  arrested,  but  is  so  altered 
in  tin-  rate  with  which  its  details  pass  before  us  that  they  may  be 
easily  observed.    (See  §  122.) 

"  Again,  experiment  often  leads  to  new  phenomena  and  to  a 
knowledge  of  activities  l)efore  unobserved.  Indeed,  by  far  the 
greater  part  of   our  knowledge  of   natural   phenomena  has  been 


38  [Elements  of  Natural  Philosophy,  pp.  1S?\ 

acquired  by  means  of  experiment.  To  be  of  value,  experiments 
must  be  conducted  with  system,  and  so  as  to  trace  out  the  whole 
course  of  the  phenomenon. 

"  Having  acquired  our  facts  by  observation  and  experiment,  we 
seek  to  find  out  how  they  are  related,  i.  e.,  to  discover  the  laws  that 
connect  them.  The  process  of  reasoning  by  which  we  discover  such 
laws  is  called  induction.  As  we  can  seldom  be  sure  that  we  have 
apprehended  all  the  related  facts,  it  is  clear  that  our  inductions 
must  generally  be  incomplete.  Hence,  it  follows  that  conclusions 
reached  in  this  way  are,  at  best,  only  probable ;  yet  their  probability 
becomes  very  great  when  we  can  discover  no  outstanding  fact,  and 
especially  so  when,  regarded  provisionally  as  true,  they  enable  us  to 
foresee  what  will  occur  in  cases  before  unknown. 

"In  conducting  our  experiments  and  our  reasonings,  we  are  often 
guided  by  suppositions,  suggested  by  previous  experience.  If  the 
course  of  our  experiment  be  in  accordance  with  our  supposition, 
there  is,  so  far,  a  presumption  in  its  favor.  So,  too,  in  reference  to 
our  reasonings  ;  if  all  our  facts  are  seen  to  be  consistent  with  some 
supposition,  not  unlikely  in  itself,  we  say  that  it,  thereby,  becomes 
probable.  The  term  hypothesis  is  usually  employed  instead  of 
supposition. 

"A  law  of  nature  can  not  be  demonstrated  in  the  sense  that  a 
mathematical  truth  is  demonstrated.  Yet  so  great  is  the  constancy 
of  uniform  sequence  with  which  phenomena  occur  in  accordance 
with  the  laws  which  we  discover,  that  we  have  no  doubt  respecting 
their  validity. 

"  When  we  would  refer  a  series  of  ascertained  laws  to  some  com- 
mon agency,  we  employ  the  term  theory.  Thus,  we  find  in  the 
1  wave  theory '  of  light,  based  on  the  hypothesis  of  a  universal  ether 
(§  608)  of  extreme  elasticity,  satisfactory  explanations  of  the  laws  of 
reflection,  refraction,  diffraction,  polarization,  etc." — Anthony  and 
Brackett. 

See  Deschanel's  "  Natural  Philosophy  "  (published  by 
D.  Appleton  &  Co.),  §§  1-5.  The  teacher  can  ill  afford  not 
to  own  this  book. 

§  5.  See  First  Principles  of  Nat.  Phil,  §§  4,  6.  Also 
Hand-Book  note  on  §  4  of  First  Prin.  Nat.  Phil 

§  6.  The  several  divisions  of  matter  may  be  defined  as 
follows : 


[Elements  of  \nturdJ  Philosophy,  p.  8.]  39 

(a.)  A  mass  is  any  portion  of  matter  that  is  divisible 
without  destroying  its  identity. 

(b.)  A  molecule  is  a  portion  of  matter  so  small  that  it 
cannot  be  divided  without  destroying  its  identity.  This 
definition  is  chemical  in  its  bearings. 

(c.)  For  the  sake  of  simplicity,  let  us  consider  the  mole- 
cules of  matter  in  a  gaseous  condition.  Then  we  may  say 
that  a  molecule  is  that  minute  portion  of  the  substance 
that  moves  about  as  a  whole  so  that  its  parts  (if  it  has 
parts)  do  not  part  company  during  the  motion  of  agitation 
of  the  gas.     This  definition  is  dynamical  in  its  bearings. 

(d.)  An  atom  is  a  portion  of  matter  supposed  to  be  in- 
capable of  division  into  parts.  (Etymologically,  atom 
means  something  that  cannot  be  cut.) 

In  some  works  written  by  eminent  physicists,  the  word  atom 
is  used  as  if  it  were  synonymous  with  molecule,  but  during  the  last 
few  years  usage  has  been  growing  more  uniform.  The  distinction 
is  now  generally  maintained.  Concerning  molecules,  the  teacher 
may  find  information  in  Todhunter's  !"  Natural  Philosophy  for 
Beginners,"  Part  I,  Chapter  LXI.  Concerning  atoms,  he  is  advised 
to  read  Lecture  XII,  of  Tait's  "  Recent  Advances  in  Physical 
Science."  Also  read  Chapter  XXII  of  Maxwell's  "Theory  of 
II.  at  ■  and  pp.  5,  6,  of  this  Hand-Book. 

Molecules  may  be  elementary  or  compound  (».  e.,  composed  of  a 
single  element  or  of  two  or  more  elements) ;  atoms  are  necessarily 
elementary.  It  is  considered  certain  that  oxygen,  hydrogen,  chlo- 
rine, nitrogen,  bromine,  iodine,  sulphur,  selenium  and  tellurium  are 
diatomic  (i  e.,  huve  two  atoms  to  the  molecule) ;  that  phosphorus 
and  arsenic  are  tetratomic  (four  atoms),  and  that  cadmium  and 
mercury  are  monatomic  (one  atom).  It  is  very  probable  that  potas- 
sium is  diatomic.  Concerning  the  atomicity  of  the  other  elements, 
nothing  is  known.     See  Elements  of  Chemist  ri/. 

While  it  is  practically  impossible  to  isolate  a  molecule,  it  may  be 
urged  that,  as  a  mmtu!  feat,  it  is  possible  to  divide  a  molecule  of 
phosphorus  into  four  atoms  of  phosphorus,  which  would  leave  the 
identity  of  the  substance  unchanged.  Still,  tin-  theoretical  concep- 
tion is  that,  in  the  free  or  uncombined  state,  the  elements  exist  as 
molecules  and  aggregations  thereof ;  th  it  when  they  enter  into 
chemical  combinations,  they  do  so  as  atoms  rather  than  as  molecule* 


40  [Elements  of  Natural  Philosophy,  p.  3.] 

This  whole  matter  (which  pertains  to  chemistry  rather  than  to 
physics)  is  so -largely  theoretical  that  it  would  not  be  wise  to  puzzle 
the  minds  of  ordinary  pupils  by  dwelling  at  any  length  upon  these 
points. 

It  is  said  that  the  smallest  living  being  visible  with  the 
aid  of  the  microscope  contains  not  more  than  a  million 
organic  molecules  and  a  million  molecules  of  water. 

It  has  been  estimated  by  Sir  W.  Thomson  and  others  that 
about  two  million  molecules  of  hydrogen  placed  in  a  row 
would  occupy  the  space  of  one  millimeter  (§  26),  and  that 
about  two  hundred  million  million  million  of  them  woul;l 
weigh  one  milligram  (§  35).  While  these  are  mere  ap- 
proximations to  accurate  determinations,  they  indicate 
that  the  determination  of  the  size  and  weight  of  a  mole- 
cule is  a  legitimate  object  of  science  and  that  they  are  not 
immeasurably  small. 

Much  has  been  written  concerning  the  ultimate  identity 
or  fundamental  diversity  of  atoms.  The  common  view  is 
that  there  are  as  many  kinds  of  atomic  matter  as  there 
are  elements,  i.  e.,  sixty-six  or  more.  But  some  able  physi- 
cists believe  that  all  of  these  apparent  diversities  result 
from  the  forms  of  atomic  motion,  or,  as  Herbert  Spencer 
says,  from  "the  compounding  and  recompounding  of 
ultimate  homogeneous  units."     Says  Thomas  Graham : 

"  It  is  conceivable  that  the  various  kinds  of  matter  now  recog- 
nized as  different  elementary  substances  may  possess  one  and  the 
same  ultimate  or  atomic  molecule  [the  meaning  is  evident  though 
the  expression  is  unfortunate]  existing  in  different  conditions  of 
movement." 

Probably  every  teacher  and  pupil  has  seen  the  rings 
produced  by  some  tobacco  smoker,  or  sent  upward  from 
the  smokestack  of  a  railway  locomotive.  See  Tait's 
"Recent  Advances  in  Physical  Science,"  p.  292.  Such 
rings  have  a  peculiar  "  vortex"  motion  by  virtue  of  which 
they  keep  their  form  distinct  from  the  air  through  which 


[Elements  of  Natural  Philosophy,  pp.  3-6.]  41 

they  are  passing.  Whatever  the  translatory  motion  of  the 
ring,  every  smoke  particle  on  the  inner  side  of  the  ring  is 
moving  forward,  and  every  such  particle  on  the  outside  of 
the  ring  is  going  backward,  bo  that  all  of  the  smoke  is  turn- 
ing round  and  round  its  linear,  circular  core.  If  the  air 
were  a  perfect  fluid  (i.e.,  if  there  were  no  fluid  friction 
in  the  air),  such  vortex  rings  would  go  on  moving  and  pre- 
serving their  form  forever.  Sir  William  Thomson  has 
offered  a  hypothetical  atom  consisting  of  vortex  rings  of  a 
universal,  perfect  fluid.  Such  a  vortex  ring  might  exist 
with  any  number  of  knots  ami  windings  upon  it.  If  two 
such  rings  were  linked  together,  they  never  could  be  sepa- 
rated, and  if  they  were  knotted  upon  themselves,  they  never 
could  be  untied.  Each  would  preserve  the  form  given  to  it 
at  the  time  of  its  creation.  The  conjecture  of  Sir  W. 
Thomson  is  that  the  different  forms  of  vortex  rings  com- 
posed of  one  homogeneous,  incompressible,  perfect  fluid, 
constitute  what  are  generally  called  atoms  and  that  differ- 
ence in  form  of  rotation  is  the  basis  of  difference  in  the 
properties  of  matter.  At  first  sight,  this  may  seem  very 
fanciful,  but  to  some  of  the  leading  physicists  of  our  day, 
"  it  appears  to  be,  by  far,  the  most  fruitful  in  consequences 
of  all  the  suggestions  that  have  hitherto  been  made  as  to 
the  ultimate  nature  of  matter. "  See  Ninth  Edition  of 
"  Encyclopaedia  Britannica,"  Vol.  Ill,  p.  43. 

§  8.  See  First  Prin.  Nat.  Phil,  §  8. 

§  11.  Dissolve  a  tablespoonful  of  white  sugar  in  a  little 
hot  water,  making  a  thick  syrup.  Place  a  teacup,  con- 
taining the  syrup,  in  a  large  platter  and  pour  upon  the 
syrup  two  or  three  times  its  bulk  of  strong  sulphuric  acid. 
The  sugar  molecule  is  represented  by  the  formula. 
C,2H220|,;  i.e.,  it  consists  of  twelve  atoms  of  carbon, 
twenty-two  of  hydrogen  and  eleven  of  oxygen.  The 
quantity  of  hydrogen  and  oxygen  in  this  one  molecule  is 
just  equal  to  that  constituting  eleven  molecules  of  water 


j 

1 1  [Elements  of  Natural  Philosophy,  pp.  5-9.] 

(11  H20  =  H220,,).  Sulphuric  acid  has  a  very  great  avidity 
for  water.  In  this  experiment,  the  acid  robs  the  sugar  of 
the  elements  of  water  and  leaves  the  carbon  as  a  black, 
bulky,  spongy  mass.  This  is  a  chemical  change,  for  the 
molecule  has  been  changed  from  sugar  to  carbon  (or 
charcoal). 

Dissolve  a  "  heaping  teaspoonful"  of  calcium  chloride 
(not  chloride  of  lime)  in  a  teaspoonful  of  warm  water.  In 
another  wine  glass,  add  half  a  teaspoonful  of  sulphuric 
acid  to  two  teaspoonfuls  of  water.  Pour  the  diluted  acid 
into  the  calcium  chloride  solution.  The  two  liquids  make 
solid  plaster-of- Paris  (calcium  sulphate). 

These  experiments  (or  either  one  of  them)  will  interest 
the  class  and  be  sufficient  for  the  purpose  intended.  Many 
more  may  be  found  in  the  Elements  of  Chemistry. 

§  24.  You  can  get  any  desired  information  concerning 
the  metric  system  or  metric  apparatus  by  addressing  the 


weighs 

(water)1 


American  Metric  Bureau,  32  Hawley  Street,  Boston. 
Enclose  a  postage  stamp  for  reply.  The  supply  depart- 
ment of  the  Bureau  distributes  the  metric  weights,  meas- 
ures, apparatus,  etc.,  at  wholesale  prices.  The  following 
is  an  extract  from  the  Constitution  of  the  Bureau: 

"The  object  of  this  Bureau  shall  be  to  disseminate  information 
concerning  the  Metric  System  ;  to  urge  its  early  adoption  ;  and  to 
bring  about  actual  introductions  wherever  practicable.  To  this  end, 
it  will  secure  the  delivery  of  addresses  ;  publish  articles  ;  circulate 
books,  pamphlets  and  charts ;  distribute  scales  and  measures ;  in- 


J 

[Elements  of  Natural  Philosophy,  pp.  D-u.]  43 

joduce  the  practical  teaching  of  the  system  in  schools  ;  and  in  nil 
proper  ways,  as  far  as  the  means  at  its  disposal  will  allow,  the 
Bureau  will  urge  the  matter  upon  the  attention  of  tin*  Americas 
people!  I'M  tney  shall  join  the  rest  of  the  world  in  the  exclusiw  BM 
of  the  International  Decimal  Weights  and  Measures," 

§25.  It  is  now  known  that  the  meter  is  not  exactly 
0.0000001  of  a  quadrant  of  the  meridian  of  Paris.  Such 
a  quadrant  is  about  10,000,850  meters.  The  meter  is, 
therefore,  an  arbitrary  standard.  It  is  represented  by  a 
certain  platinum  bar  at  Paris. 

§  31.  See  Danieirs  "  Principles  of  Physics,"  p.  203. 

§32.  Porous  corks  maybe  made  air  and  water  tight 
by  holding  them  for  five  minutes  beneath  the  surface  of 
melted  parafrine  wax.  The  paraffine  may  be  had  at  the 
druggist's.  The  corks  may  be  held  down  in  the  liquid  by 
a  perforated  cover  or  wire  screen.  A  simple  experiment  to 
illustrate  the  impenetrability  of  air  is  to  invert  a  tumbler 
in  a  basin  of  water.  It  can  be  seen  that  the  water  does 
not  fill  the  tumbler.  Of  course  it  will  compress  the  air. 
(£§  227,  284.)  Then  thrust  a  wad  of  coarse  brown  (or 
filter)  paper  into  a  glass  tube,  asalamp-chimnev,  close  one 
end  with  the  hand  and  immerse  the  tube  in  water,  holding 
the  open  end  downward.  That  the  water  does  not  enter 
the  tube  while  the  hand  closes  the  up]K?r  end  may  be  seen 
directly,  or  from  the  fact  that  the  paper  wad  remains  dry. 

See  First  Prin.  Nat.  Phil,  Fig.  2. 


44  [Elements  of  Natural  Philosophy,  p.  14.] 

Exercises,  Page  14. 

1.  A  liter  =  1  cu.  dm.  =  1000  cu.  cm.  One  cu.  em.  of 
pure  water  weighs  1  gram ;  1000  cu.  cm.  weigh  1000  grams, 
or  1  Kg. 

2.  1000  g.  x  1.8  =  1800  g. 

3.  1250  cu.  cm.  of  water  weigh  1250  g. 
1250  g.  x  .8  =  1000  g.  or  1  A#. 

4.  Since  a  liter  of  water  weighs  1000  g.,  250  #.  of  water 
is  J  of  a  liter  of  water. 

5.  1  cu.  dm.  p  1000  cu.  cm.  1  cu.  dm.  of  water,  there- 
fore, weighs  1000  g.  =  1  A#. 

6.  1  liter  =  1000  cu.  cm.;  1  dl.  =  100  ew.  cm.  1  e#.  of 
water  weighs  100  times  1  g.  =  100  g.  =  1  J^r. 

The  following  is  well  calculated  to  show  the  great  con- 
venience of  the  metric  system  of  weights  and  measures: 
Required  to  find  the  capacity  of  some  small,  irregular 
cavity  in  a  solid.  Weigh  the  solid.  Then  fill  the  cavity 
with  mercury  and  weigh  the  solid  again.  The  difference 
between  the  two  weights  will  be  the  weight  of  the  mer- 
cury. This  weight,  in  grams,  divided  by  13.6  [§  253  (2)] 
will  give  the  number  of  grams  that  the  same  bulk  of 
water  will  weigh  and.  therefore,  the  capacity  of  the  cavity 
in  cubic  centimeters  (§  36). 

§  37.  When  a  candle  burns,  it  disappears.  To  show 
that  the  matter  of  the  candle  has  not  been  destroyed, 
support  a  tin  basin  of  water  containing  ice  above  the  flame 
so  that  the  tip  of  the  flame  shall  just  touch  the  middle  of 
the  bottom  of  the  basin.  Protect  the  flame  from  disturb- 
ance by  air  currents.  In  about  10  minutes,  examine  the 
bottom  of  the  basin.  Whence  the  carbon  (soot)  and  the 
water  ?  The  carbon  came  from  the  candle.  Part  of  the 
water  (H20)  came  from  the  same  source,  the  hydrogen  of 
the  candle  uniting  (in  a  chemical  process,  §  11)  with  the 
oxygen  of  the  air  to  form  steam.     This  steam  was  con- 


[Memento  of  Natural  Philosophy,  pp.  1M&]  45 

densed  to  water  by  the  cold  metal  with  which  it  came  info 
contact  See  EbmenU  of  Chemistry,  Exps.  57,  169-171 
and  *•  Popular  Science  News,"  Vol.  20,  p.  92. 

§  41.  Opposed  to  the  commonly  accepted  theory  that 
bodies  arc  made  up  of  atoms  is  the  theory  of  the  homo- 
geneity and  continuity  of  bodies.  This  asserts  thai  as  a 
drop  of  water  (or  other  inorganic  body)  may  be  divided 
into  two  parts  each  of  which  is  a  drop  of  water,  so  these 
smaller  drops  may  be  again  divided  and  that  there  is 
nothing  in  the  nature  of  things  why  this  process  of*  divi- 
sion may  not  be  repeated  again  and  again,  times  without 
end.  This  theory  of  the  infinite  divisibility  of  bodies  is 
in  direct  contradiction  to  the  atomic  theory.  It  is  not 
evident  how  the  former  can  be  reconciled  with  the  ob- 
served facts  of  the  compressibility  and  interpenetrability  of 
bodies,  which  properties  of  matter  are  easily  explained  on 
the  theory  of  intermolecular  spaces  occupied  by  a  highly 
elastic  medium  called  the  ether. 

§  42.  See  First,  Prin.  Nat.  Phil,  Exps.  15,  16,  aud 
Deschanel's  "  Natural  Philosophy,"  §§  21,  22,  23. 

§  44.  See  First  Prin.  Nat.  Phil,  Exp.  17. 

§  45.  See  First  Prin.  Nat.  Phil..  Exp.  18. 

§  46.  See  First  Prin.  Nat.  Phil,  Exp.  19. 

§  47.  See  First  Prin.  Nat,  Phil,  Exp.  20. 

§  51.  See  First  Prin.  Nat.  Phil,  Exp.  21. 

§  54.  All  solid,  unorganized  bodies  are  crystalline  or 
amorphous.  Crystalline  bodies  are  characterized  by  reg- 
ularity of  form  ;  amorphous  bodies  exhibit  no  such  reg- 
ularity. Freedom  of  molecular  motion  is  necessary  for 
the  formation  of  crystals.  When  crvstallizable  bodies 
slowly  solidify  from  the  liquid  or  gaseous  conditions,  the 
molecules  arrange  themsi -Ives,  under  the  influence  of  the 
mysterious  structural  forces,  according  to  one  of  six  min- 


46  [Elements  of  Natural  Philosophy,  pp.  21,  22. ~\ 

eralogical  systems  of  crystals.  Such  molecular  motion 
and  arrangement  sometimes  take  place  in  solids,  under  the 
influence  of  friction,  percussion,  etc.  Thus  the  jarring 
of  continued  use  often  renders  railway  car  axles,  crystal- 
line and  brittle.  Such  facts  lead  us  to  ascribe  a  definite 
structural  form  to  such  molecules,  determining  special 
points  of  application  for  the  molecular  forces.  Amorphous 
bodies'  that  cannot,  under  any  known  circumstances, 
assume  the  crystalline  form  are  called  colloids. 

§  55.  Thomas  Young  has  shown  that  a  liquid  may  be 
treated  as  if  it  were  covered  at  the  bounding  surface  with 
a  stretched  membrane  with  a  constant  tension  tending  to 
contract  it.  Hence,  every  free  liquid  moves  so  that  its 
bounding  surface  shall  be  as  small  as  possible ;  i.  e.,  it 
assumes  the  spherical  form.  This  is  familiarly  shown  in 
drops  of  falling  water  and  in  globules  of  mercury.  Pla- 
teau illustrated  the  same  fact  on  a  larger  scale  by  placing 
a  mass  of  oil  in  a  mixture  of  alcohol  and  water,  carefully 
adjusted  to  have  the  same  specific  gravity  as  the  oil.  The 
oil  then  had  no  tendency  to  translatory  motion  under  the 
influence  of  gravity,  but  was  left  free  to  arrange  itself 
\mder  the  free  action  of  the  molecular  forces.  The  freely 
floating  mass  at  once  assumed  the  spherical  form. 

§  59.  It  is  proper  to  add  that  there  is  no  sharp  line  of 
distinction  between  the  three  conditions  of  matter  such  as 
our  definitions  imply.  Bodies  present  all  forms  of  molec- 
ular aggregation  and  often  pass  from  gas  to  liquid  or  from 
liquid  to  solid  by  imperceptible  gradations. 

(a.)  Oxygen  was  liquefied  at  a  temperature  of —  140°  C.  (§  546) 
arrl  under  a  pressure  of  320  atmospheres  (§  277).  When  a  jet  of 
this  liquid  escaped  into  the  air,  it  was  partly  solidified.  Hydrogen 
was  similarly  liquefied  under  a  pressure  of  650  atmospheres.  For 
full  accounts  of  the  liquefaction  of  "the  permanent  gases,"  see 
"The  Popular  Science  Monthly,"  "The  Scientific  American,"  or 
the  English  paper,  "  Nature,"  for  the  year  1878. 

(&.)  See  First  Prin.  Nat.  Phil.,  §  43  (a).     Also,  Exp.  25. 


[Elements  of  Natural  Philosophy,  p.  24.]  I  j 

§  62.  The  colliding  molecules  of  a  gas  are  supposed  to 
act  on  each  other  only  within  very  short  distances  and  for 
MTv  short  times  before  and  after  collision.  Their  motions 
are  free  and,  therefore,  rectilinear  in  the  intervals.  The 
average  distance  between  such  actions  is  called  the  mean 
free  path  of  the  molecule.  These  paths  lie  in  all  conceiv- 
able directions.  The  intervals  of  time  between  the  en- 
counters are  indefinitely  long  in  comparison  with  the 
duration  of  tbe  collisions.  Three  kinds  of  experiments 
indicate  that,  at  a  pressure  of  one  atmosphere  and  at  the 
temperature  of  melting  ice,  the  mean  free  path  of  a  hydro 
gen  molecule  is  about  0.0001  millimeter,  or  about  0.2  the 
length  of  a  wave  of  green  light  (§  717).  The  mean  free 
path  of  other  molecules  is  less  than  that  of  hydrogen. 

In  the  introductory  paragraph  of  this  Hand-Book,  we 
have  considered  the  definition  of  hypothesis.  It  may  be 
well,  right  here,  to  ask  ourselves,  What  is  an  explanation  t 

"  Every  act  of  explanation  consists  in  detecting  and  pointing  out 
a  resemblance  between  facts  or  in  showing  that  a  greater  or  less 
degree  of  identity  exists  between  apparently  diverse  phenomena. — 
J>  cons. 

"  When  a  new  phenomenon  presents  itself,  the  question  arises  in 
the  mind  of  the  observer :  What  is  it?  This  question  means:  Of 
what  known,  familiar  fact  is  this  apparently  strange,  hitherto  un- 
known fact,  a  new  presentation,— of  what  known  familiar  fact  or 
facts  is  it  a  disguise  or  complication?  All  explanation,  including 
explanation  by  hypothesis,  is,  in  its  nature,  classification." — Stallo. 

"The  business  of  science  is  simply  to  ascertain  in  what  manner 
phenomena  coexist  with  each  other  or  follow  each  other,  and  the 
only  kind  of  explanation  with  which  it  can  properly  deal  is  that 
which  refers  one  set  of  phenomena  to  another  set."— Fiske. 


CHAPTER  II. 

The  teacher  will  probably  find  that  the  section  on  Force 
and.  Motion,  at  the  beginning  of  this  chapter,  is  difficult 
for  the  pupils  at  this  stage  of  their  progress.  The  author 
would  have  placed  it  in  the  latter  part  of  the  book,  had 
not  its  very  nature  demanded,  that  it  be  placed,  where  it  is. 
He  would  advise  that  it  be  taken  in  course,  but  that  its 
complete  mastery  be  not  insisted  upon  until  the  review. 
Such  a  review  should  be  had  before  Chapter  III  is  begun. 
"  The  advance  in  knowledge  which  an  individual  student 
obtains  by  the  devotion  of  time  and  attention  to  a  science, 
is  similar  in  character  to  the  progress  which  the  science 
itself  makes  in  the  course  of  ages ;  the  student  can  trace 
his  way  backward  to  a  clearer  view  of  the  first  principles, 
and  forward  to  more  extensive  developments  and  appli- 
cations. " 

§  63.  "  Dynamics  is  the  science  which  treats  of  the  action  of 
force.  The  name  is  derived  from  the  Greek  word  dynamis,  meaning 
force.  Within  the  last  twenty  years,  many  improvements  have  been 
made  in  the  nomenclature  employed  in  this  science.  The  name 
Mechanics,  which  properly  denotes  the  science  of  machines,  and 
was  used  by  Newton  in  that  sense,  came  for  a  time  into  use,  instead 
of  the  appropriate  word,  Dynamics,  for  the  science  which  treats  of 
force  ;  and  under  that  name  there  was  a  peculiar  '  cross-division  of 
the  subject  into  Statics  and  Dynamics,  in  which  the  proper  signifi- 
cation of  the  latter  name  was  altogether  departed  from.'  The 
change  to  a  better  nomenclature  has  recently  been  made. " — Bottomley. 

Physical  science  accepts  a  dynamical  interpretation  as 
the  best  explanation  of  all  physical  phenomena. 

"  The  object  of  the  natural  sciences  is  to  find  the  motions  upon 
which  all  other  changes  are  based  and  their  corresponding  motive 
forces." — Helmholtz. 


[Elements  of  Natural  Philosophy,  pp.  25-20.]  49 

"  When  a  physical  phenomenon  can  be  completely  described  as  a 
change  in  the  configuration  and  motion  of  a  material  system,  the 
dynamical  explanation  of  that  phenomenon  is  said  to  be  complete. 
We  cannot  conceive  any  further  explanation  to  be  necessary,  desir- 
able or  possible,  for  as  soon  as  we  know  what  is  meant  by  the  words 
configuration,  mass  and  force,  we  see  that  the  ideas  which  they 
represent  are  so  elementary  that  they  cannot  be  explained  by  means 
of  anything  else." — Clerk  Maxwell. 

"Physical  science  is  a  resolution  of  the  phenomena  of  nature  into 
atomic  mechanics.  It  is  a  fact  of  psychological  experience  that, 
whenever  such  a  reduction  is  successfully  effected,  our  craving  for 
causality  is,  for  the  time  being,  wholly  satisfied."— Emil  du  Bois 
Beymond. 

Stallo  speaks  of  the  claim  that  "modern  physical  science  is 
throughout  a  partial  and  progressive  solution  of  the  problem  of 
reducing  all  physical  phenomena  to  a  system  of  atomic  mechanics." 

The  kinetic  theory  of  gases,  for  example,  is  valuable  and 
satisfactory,  chiefly  because  it  affords  consistent  ground 
for  the  dynamical  interpretation  of  the  phenomena  to 
which  it  relates.  The  "  action  at  a  distance  "  explanations 
&f  gravitation  and  electric  attraction  are  unsatisfactory 
chiefly  because  they  do  not  thus  deal  with  the  phenomena 
to  which  they  pertain. 

See  DeschanePs  "Natural  Philosophy,"  §  6. 

§  64.  See  Tait's  "Heat,"  Chap.  3. 

§  69.  The  force  that,  acting  for  one  second  on  a  mass 
of  one  pound,  produces  a  velocity  of  one  foot  per  second, 
is  called  z,  poundal.  As  the  increment  of  velocity  due  to 
gravity  (§  127)  is  32.16  ft.,  the  weight  of  a  pound-mass 
equals  32.16  poundals.  In  the  text  and  here,  when  we  use 
the  word  "weight,"  we  mean  the  force  exerted  by  the 
force  of  gravity  on  the  mass  in  question. 


50  {Elements  of  Natural  Philosophy.} 

Exercises,  Page  30. 

1.  500  X  500  ==  250,000. 

2.  321.6  x  200  =  64,320. 


■■\ 


.„  X  ^       ^  !•  Their  momenta  are  equal 
10  x  2  =  20  J  * 


4.  Gee  §  67  (a.)  and  §  68. 

32.16  x  10  =  321.6. 

5.  There  are  5280  ft.  in  a  mile. 

5280  x  15  x  1  _ 
1320  x  12 

The  momentum  of  the  ball  will  be  5  times  that  of  the 
stone. 

n     (  50,000  x    2  =  100,000  )  mi    •  i  i 

6.  1  *    ™"      *1       .L\™  r  Their  momenta  are  equaL 
( 10,000  x  10  =  100,000  J  M 

7.  25  x  60  =  1500,  the  momentum  of  the  first,  and, 
consequently,  of  the  second.  1500  -=-  40  =  37.5.  The 
velocity  of  the  second  is  37.5  ft.  per  second. 

8.  100  x  20  =  2000. 

2000  -r-  500  =  4.    Velocity  =  4  m.  per  second. 

10.  See  §  69. 

12  x  6  =  72,  the  number  of  dynes. 

12.  We  must  consider  the  attracting  force  to  be  uni- 
formly y^  dyne.  As  a  matter  of  fact,  this  would  not  be 
true.  See  §  100  (2).  A  force  of  1  dyne  would  give  to  the 
body  weighing  1  gram,  a  velocity  of  1  cm.  per  second. 
(§  69.)  Then  a  force  of  y^  dyne  would  give  it  a  velocity 
of  yJ¥  of  1  cm.  =  .1  mm.  A  body  100  times  as  heavy 
would  be  moved  by  the  same  force  with  yfg-  of  this  velocity, 
or  .001  mm. 


[Element*  of  Natural  PhUog.yhy,  pp.  51 

§  73.  "  If  we  conceive  of  a  body  moving  in  empty  space,  we  can 
think  of  no  reason  why  it  should  alter  its  path  or  its  rate  of  motion 
in  any  way  whatever." — Anthony  and  Brackett. 

§  74.  See  Frick's  "  Physical  Technics/'  pp.  58-61,  and 
Deschanel's  Nat.  Phil.,  §§  49-51. 

§  84.  See  Frick's  "  Physical  Technics,"  pp.  58-61. 

§  86.  Two  equal  forces  acting  in  opposite  directions 
along  parallel  lines  cannot  be  balanced  by  any  single  force. 
They  constitute  what  is  called  a  couple.  The  moment  of  a 
couple  is  the  product  of  the  numbers  representing  respect- 
ively the  magnitude  of  one  of  the  forces  and  the  perpen- 
dicular distance  between  the  lines  ^^____^^ 
of  the  two  forces.    Two  couples  ap-     /ffy\  ^^***v 

plied  to  the  same  rigid  body  will   /  t \^  g\ 

balance  if  their  planes  are  coinci-  t  A  \        """.''  J 

dent  or  parallel,  their  moments  are   \.  \/^/^ 

equal  and  if  they  are  applied  so  as       ^ y 

to  turn  the  body  round  in  opposite  directions.  Thus,  the 
couple  composed  of  the  forces,  F  and  /  will  balance  the 
couple  G  and  g,  if  F  x  A  B  =  G  x  C  I). 

The  direct  tendency  of  a  couple  is  to  produce  rotation 
of  the  body  to  which  it  is  applied.  The  turning  of  a  key 
in  a  lock  affords  a  familiar  example  of  a  couple,  the  shaft 
of  the  key  serving  to  transmit  the  effect  of  the  couple 
acting  on  the  handle.     See  §  171. 

§  92.  See  Deschanel's  "  Natural  Philosophy,''  §  16. 

§  93.  "  When  two  bodies  interact  so  as  to  produce,  or  tend  to 
produce,  motion,  their  mutual  action  is  called  a  stress.  If  one  body 
be  conceived  as  acting  and  the  other  as  beinjr,  acted  on,  the  stress, 
regarded  as  tending  to  produce  motion  in  the  body  acted  on,  is  a 
force.  The  third  law  of  motion  states  that  all  interaction  of  bodies 
is  of  the  nature  of  stress  and  that  the  two  forcrs  into  which  the 
stress  can  be  resolved  are  equal  and  oppositely  directed.  From  this 
follows  directly  the  deduction  that  the  total  momentum  of  a  system 
is  unchanged  by  the  interaction  of  its  parts  ;  that  is.  the  momentum 


52  [jileme?Ui*  of  Natural  Philosophy,  pp.  42,  4$.] 

gained  by  one  part  is  counterbalanced  by  the  momentum  lost  by  the 
others.  This  principle  is  known  as  the  conservation  of  momentum," 
—Anthony  and  Brackett. 

§  95.  See  First  Prin.  Nat  Phil,  Exp.  32. 


[Elements  of  Natural  Philosophy.]  53 

Exercises ,  Page  44. 

1.  Adopt  any  convenient  scale,  as  1  mm.  to  the  lb. 
Then  would  the  force  of  100  lb.  be  represented  by  a  line 
10  cm.  long,  and  the  other  force  by  a  line  15  cm.  long. 
See  §  80  (1).  The  resultant  would  be  represented  by  a 
line  25  cm.  long. 

&  See  §  80  (2).  The  resultant  would  be  represented  by 
a  line  5  cm.  long  (if  we  adopt  the  same  scale  as  above) ; 
motion  will  be  in  the  direction  of  the  greater  force. 

3.  Suppose  we  adopt  the  scale  of  an  inch  to  the  mile. 
Draw  a  horizontal  line  4  inches  long  to  represent  the  force 
of  the  oars.  From  one  end  of  this  line,  draw  a  vertical 
line  3  inches  long  to  represent  the  force  of  the  current. 
Join  the  free  ends  of  these  lines ;  the  hypothenuse  thua 
formed  will  represent  the  resultant  of  these  two  forces. 

32  +  42  =  25.     a/25  =  5. 

See  §  85.  The  boat  will  move  in  the  direction  indicated 
by  the  hypothenuse  and  with  a  velocity  of  5  miles  per 
hour.  Of  course,  the  problem  means  that  the  boat  is 
headed  directly  across  the  stream. 

4.  Draw  a  vertical  line,  64  units  (as  mm.,  or  16ths  of  an 
inch)  long.  From  the  foot  of  this  line  draw  a  horizontal 
line  24  units  long.  (Use  the  same  kind  of  units  that  you 
adopted  for  the  vertical  line.)  Join  the  free  ends  of  these 
lines.  The  hypothenuse  will  be  the  graphic  representa- 
tion of  the  resultant. 


642  -f  242  =  4672.     \/4672  =  68+. 

5.  Draw,  as  before,  a  vertical  line  (3  x  20  =)  60  units 
long,  and  a  horizontal  line  (12  x  20  =)  240  units  long. 
Draw  the  hypothenuse. 

60s  +  2402  =  61200.     \/61200  =  247+. 


54 


[Elements  of  Natural  Philosophy,  p.  45.] 


6.  See  §  68  (a).  804  kinetic  units  =  25  gravity  units, 
Draw  BN  =  10  units  of  length.  From  B,  draw  BE  at 
right  angles  to  BN  and  make  it  15  units  long.  Complete 
the  parallelogram   and  draw  the   partial  resultant,   Br. 


From  B,  dfaw  BS  at  an  angle  of  45°  from  BE  and  make 
it  25  units  long.  Complete  the  parallelogram  and  draw 
the  diagonal,  BR,  which  will  represent  the  complete 
resultant. 

The  line,  BN,  being  taken  2  cm.  long,  the  scale  here 
adopted  is  2  mm.  per  pound.  The  line,  BR,  being  67  mm. 
long,  represents  a  force  of  35^  lb.  or  1141.68  absolute 
units.  Some  weight  may  be  assumed  for  the  ball.  The 
resultant  must  be  assumed  to  act  for  some  definite  time, 
say  one  second.  Dividing  the  number  of  absolute  units 
(1141.68)  by  the  number  of  pounds,  gives  us  the  velocity 
imparted  to  the  ball  by  the  resultant  force  in  one  second. 
This  velocity  multiplied,  in  its  turn,  by  the  same  number 
of  pounds,  gives  us  the  momentum.  As,  in  this  operation, 
we  use  the  weight  successively  as  divisor  and  multiplier, 
its  value  is  of  no  account  in  the  solution  of  the  problem, 


[Elements  of  Xatural  Philosophy,  p.  45.]  55 

as  it  would  be  if  velocity  and  not  momentum  were  called 
for.  The  greater  the  weight,  the  lest*  the  velocity  and 
versa,  their  product  (momentum)  remaining  the  same. 
The  number  of  absolute  units  represents  the  momentum 
also. 

7.  See  §  72  (3).  The  momentum  of  the  gun  is  equal 
to  the  momentum  of  the  projectile.  As  the  gun  is  heavier 
than  the  projectile,  its  velocity  must  be  less  than  that  of 
the  projectile,  in  order  that  the  products  of  the  numbers 
representing  the  weight  and  velocity  in  each  case  may  be 
equal 

8.  The  width  of  the  river  is  represented  by  a  line  4 
units  long  ;  the  actual  course  of  the  boat  by  a  line  5  units 
long.  If  the  4  units  represent  1  mile,  the  5  units  will 
represent  1  j  miles,  the  distance  that  the  boat  moves.  It 
takes  no  longer.     See  §  78. 

9.  See  Fig.  55,  in  which  LM  represents  the  plank  and 
MN,  the  distance  that  one  end  of  it  is  raised.  A  C  repre- 
sents the  gravity  or  weight  of  the  cask.  (Gravity  acts  in 
a  vertical  direction.)  From  A,  draw  AD  perpendicular  to 
LM.  From  C,  draw  CD  parallel  to  LM.  Complete  the 
parallelogram,  A  BCD.  The  force  of  gravity  represented 
by  A  C  may  be  resolved  into  two  components,  represented 
by  AD  and  AB.  AB  represents  the  force  with  which  the 
rask  tends  to  roll  down  the  plank.  This  tendency  may 
be  successfully  resisted  by  a  force  represented  by  AB', 
equal  to  AB  and  opposite  in  direction.  AB  =  \AC,  as 
may  be  seen  by  direct  measurement  or  as  may  be  proved 
geometrically,  the  triangles  ABC  said  LNM  being  similar. 
il'  nee,  the  muscular  force  needed  is  25  lb. 

10.  See  §  68.  32.16  x  60  =  1929.0,  the  number  of 
F.  I\  S.  units. 

11.  See  §  69.     60  Kg.  —  6000  g. 

980  dynes  x  6000  =  5880000  dynes. 


56  [Elements  of  Natural  Philosophy,  p.  46.] 

§98.  Whether  this  "attractive  force"  is  a  property 
inherent  in  matter  or  is  a  secondary  phenomenon,  a  result 
of  unexplained  action  of  some  kind,  is  a  theme  on  which 
much  has  been  ably  written.  The  latter  is  probably  the 
fact. 

"  All  physical  action  is  by  impact  ;  action  at  a  distance  is  impos- 
sible ;  there  are,  in  nature,  no  pulls  but  only  thrusts." 

The  reduction  of  the  phenomena  of  celestial  motion  to 
the  principle  of  universal  gravitation  was  first  made  by 
Sir  Isaac  Newton.  But  Newton  himself  did  not  believe 
the  mutual  attraction  of  bodies  to  be  an  attribute  of 
matter,  essential  thereto  and  inherent  therein.     He  says  : 

"  The  reason  of  these  properties  of  gravity  I  have  not,  as  yet. 
been  able  to  deduce,  and  I  frame  no  hypotheses."  Again:  "That 
gravity  should  be  innate,  inherent  and  essential  to  matter,  so  that 
one  body  may  act  on  another  at  a  distance,  through  a  vacuum,  with- 
out the  mediation  of  anything  else  by  and  through  which  theii 
action  may  be  conveyed  from  one  to  another,  is  to  me  so  great  an 
absurdity  that  I  believe  that  no  man  who  has  a  competent  faculty  oi 
thinking  in  philosophical  matters  can  ever  fall  into  it.  Gravity 
must  be  caused  by  an  agent  acting  constantly  according  to  certain 
laws,  but  whether  this  agent  be  material  or  immaterial  I  have  left 
to  the  consideration  of  my  readers." 

Newton  comes  very  near  framing  a  hypothesis  when,  in  speaking 
of  the  luminiferous  ether,  he  asks  :  "  Is  not  this  medium  much  rarer 
within  the  dense  bodies  of  the  sun,  stars,  planets  and  comets 
than  in  the  empty  celestial  spaces  between  them  ?  And,  in  passing 
from  them  to  great  distances,  doth  it  not  grow  denser  and  denser 
perpetually  and  thereby  cause  the  gravity  of  those  great  bodies 
towards  one  another  and  of  their  parts  towards  the  bodies,  every 
body  endeavoring  to  go  from  the  denser  parts  of  the  medium 
towards  the  rarer  ?  " 


[Elements  of  Natural  Philosophy,  p.  /,';.]  57 

One  of  Newton's  contemporaries  said  that  the  two  sup- 
positions  of  an  attractive  faculty  and  a  perfect  void  are 
"revolting";  others  were  equally  emphatic.  D'Alembert 
attributed  the  phenomena  to  that  class  of  motion-pro- 
ducing causes  the  real  nature  of  which  is  unknown  in 
contradistinction  to  action  by  impact  of  which  we  have  a 
clear  mechanical  conception.  James  Croll  affirms  that 
no  principle  will  ever  be  generally  received  that  stands  in 
opposition  to  the  old  adage,  "  A  thing  can  not  act  where  it 
is  not,"  anymore  than  it  would  were  it  to  stand  in  oppo- 
sition to  that  other  adage,  "A  thing  can  not  act  before  it 
is  or  when  it  is  not." 

"  It  is  impossible  to  conceive  what  is  called  an  attractive  force  in 
the  strict  sense  of  the  terra,  that  is,  to  imagine  an  active  principle 
having  its  seat  within  the  molecules  and  acting  without  a  medium 
through  an  absolute  void.  This  amounts  to  an  admission  that  bodies 
act  upon  each  other  at  a  distance,  i.  e.,  where  they  are  not ;  an 
absurd  hypothesis— equally  absurd  in  the  case  of  enormous  and  in 
that  of  very  small  distances." — Secchi. 

Numerous  hypotheses  have  been  framed  in  which  gravi- 
tation is  referred  to  a  wave  motion  of  an  elastic,  interstel- 
lar and  interatomic  fluid,  similar  to  the  luminiferons 
ether  or  identical  with  it. 

"  All  attempts  yet  made  to  connect  gravitation  with  the  luminif- 
erous  ether  or  the  medium  required  to  explain  electric  and  magnetic 
distance-action  have  completely  failed,  so  that  we  are  apparently 
driven  to  the  impact  theory  as  the  only  possible  one." — Stewart  and 
Tail. 

J.  B.  Stallo  says  that  the  only  impact  theory  seriously  discussed 
by  modern  physicists  and  astronomers  is  that  of  Le  Sage,  and  this, 
on  account  of  "the  extravagance  of  its  assumptions,"  he  character- 
izes as  "  a  survival  of  the  fancies  of  an  age  in  which  the  functions 
of  a  scientific  theory  were  imperfectly  understood."  He  states 
Le  Sage's  theory  thus :  "  Space  is  constantly  traversed  in  all  directions 
by  streams  of  infinitely  small  bodies  moving  with  an  almost  infinite 
velocity  and  coming  from  unknown  regions  of  the  universe.  These 
bodies  are  termed  'ultramundane  corpuscles.'  By  reason  of  th«ir 
minuteness,  they  rarely  if  ever  collide  and  the  greater  part  of  them 


58  [Elements  of  Natural  Philosophy,  p.  46.] 

find  ready  passage  through  ordinary  sensible  bodies  so  that  all  parts 
of  these  bodies — those  on  the  interior  as  well  as  those  on  the  sur- 
face— are  equally  liable  to  be  struck  by  the  corpuscles,  the  force  of 
the  impact  being  thus  proportional,  not  to  the  surfaces  but  to  the 
masses  of  the  bodies.  A  single  body  or  particle  would  be  equally 
battered  by  these  corpuscles  on  all  sides ;  but  any  two  bodies 
act  as  mutual  screens,  sr>  that  each  receives  a  less  number  of 
impacts  on  the  side  facing  the  other.  They  are,  consequently, 
driven  toward  each  other.  The  motion  of  the  corpuscles  being  rec- 
tilinear in  all  directions,  the  diminution  of  pressure  thus  resulting 
is  inversely  as  the  squares  of  the  distances  between  the  bodies 
affected." 

In  the  Ninth  Edition  of  "  Encyclopaedia  Britannica,"  Vol.  Ill,  p.  47 
which  see),  J.  Clerk  Maxwell,  speaking  of  Le  Sage's  theory,  after 
pointing  out  its  inability  to  account  for  the  temperature  of  bodies 
remaining  moderate  while  their  atoms  are  exposed  to  this  corpus- 
cular bombardment,  as  well  as  other  important  shortcomings,  says : 
u  This  theory  is  ingenious  and  is  the  only  theory  of  the  cause  of 
gravitation  that  has  been  so  far  developed  as  to  be  capable  of  being 
attacked  and  defended." 

We  have  thus  considered  the  difficulty  in  the  way  of 
accounting  for  the  phenomena  of  gravitation  at  consider- 
able length  on  account  of  its  own  immediate  importance 
and,  not  less,  for  the  reason  that  it  opens  up  to  view 
several  of  the  more  important  concepts  and  theories  of 
modern  physics.  With  these,  it  is  important  that  the 
teacher  become  as  familiar  as  the  time  at  his  disposal  will 
permit,  but  he  must  exercise  good  judgment  in  the  matter 
of  opening  up  such  polemical  topics  to  his  classes.  Most 
young  pupils  would  have  their  ideas  beclouded  rather 
than  clarified  by  the  attempt  to  give  intelligent  consid- 
eration to  such  themes. 


{Elements  of  Natural  Philosophy,  pp.  47,  48.]  59 

§  102.  See Deschanel's  "Natural  Philosophy,"  §§52,53. 

§  103.  It  is  demonstrable  that,  considering  the  earth 
as  a  hollow  sphere,  a  body  would  be  in  equilibrium  unij- 
where  within  the  shell  ;  the  attraction  in  all  directions 
would  be  equal,  whether  the  body  be  at  the  centre  or  not. 
The  subterranean  investigations  recorded  by  Ed  wan  I 
Everett  Hale,  in  his  story  of  "John  Whopper,  the  News- 
boy,* are  consistent  with  the  facts  of  gravitation. 

§  104.  It  is  to  be  borne  in  mind  that  this  paragraph 
B881  lines  "the  earth's  density  to  be  uniform."  The  den- 
sity of  the  earth  as  a  whole  is  believed  to  be  twice  that  of 
an  ordinary  mountain  upon  its  surface,  or  about  5£  times 
that  of  water.  The  interior  parts  of  the  earth  certainly 
are  more  dense  than  the  exterior  parts.  Bodies  actually 
weigh  more  as  we  descend  for  some  distance  below  the 
earth's  surface.  The  full  and  mathematically  accurate 
treatment  of  this  subject  would  be  beyond  the  province  of 
an  elementary  text-book.  A  brief  presentation  of  the 
subject  will  be  found  in  Anthony  and  Brackett's  "  Physics, " 
Part  I,  page  82. 


60  [Elements  of  Natural  Philosophy.] 

Exercises,  Page  49, 

The  teacher  will  be  particularly  fortunate  who  finds  that  all 
of  his  pupils  are  able  to  handle  a  proportion  intelligently  and 
easily.  Be  sure  concerning  this  ability  before  going  any  further  ; 
secure  it  if  possible.     Frequently  vary  the  form  of  the  statement 

from  a  :b  =  c  :  d  to  -  =  - . 
o         a 

2.  4000  —  3000  =  1000,  the  number  of  miles  from  the 

earth's  centre. 

w:  W  ::  d  :  D. 

w  :  550  ::  1000  :  4000.     /.  w  =  137J. 

3  75*  _  5625  _ 

502  -  2500  "~  *' 

4.  If  the  first  and  second  were  at  equal  distances  from 
the  third,  the  first  would  have,  on  account  of  its  lesser 
mass,  only  f  or  |  as  great  an  attraction  as  the  second. 
But  being  only  half  as  far  distant,  its  attraction  is  four 
times  as  great  as  it  would  be  if  it  were  at  an  equal  dis- 
tance, f  x  4  =  f .  The  smaller  ball  exerts  2f  as  much 
force  upon  the  third  ball  as  the  larger  one  does. 

/6       502       8  ,  (9:6),  8\ 

\9XW>  =  r°Tl:X::  1252:504'  ?>met*=l} 

5.  w  :  W  ::  D* :  d2.        w,:  900  ::  40002 :  120002. 

.%  w  =  100,  the  number  of  pounds. 

Or,  the  distance  from  the  earth's  centre  being  increased 
threefold,  the  weight  will  be  divided  by  32  or  9. 

900  lb.  -f  9  rs  100  lb. 

6.  w  :  W  : :  D2 :  d2. 

1  :  16  ::  40002 : d2. 

/.  d  =  16,000,  the  number  of  miles  from  the  earth's 
centre. 

16,000  —  4,000  =  12,000,  the  number  of  miles  from 
the  earth's  surface. 


[Elements  of  Natural  Philosophy,  p.  49.]  61 

7.  w  :  W.  =  D>  :  dK 

w  :  200  lb.  =  40002  :  70003. 


w' :  100  lb.  =  4000*  :  7000*. 

.-.  w  =  65.3    lb.,  the  man's  weight. 
.-.  w  =  32.65  lb.,  the  boy's  weight. 

Difference  in  their  weights  =  32.65  lb. 

8.  Answers,    (a.)  80  1b.  (b.)  90  1b. 

9.  Work  as  in  preceding  examples,  or  as  follows: 

50  lb.  x  H  =  32  lb-> tne  weight  1000  miles  above  the 
surface. 

50  lb.  x  I  =  37J  lb.,  the  weight  1000  miles  below  the 
surface. 

It  would  weigh  5  £  lb.  more  when  below  the  surface. 

10.  It  would  be  i  as  great  in  either  case.     See  §  100  (2) 

11.  Work  as  in  preceding  cases,  or  as  follows  : 

4000  miles  xj}  =  3750  miles. 

H      **        1?29    -  (4Q00)8 
W  ~   d*     '"'  2700  ~       d*     ' 

m  4  _    4000  x  4000       ,   1        1000  x  4000 

*'  9  "  cP  '*'  9  "  ~«P 

.-.  d*  =  36000000. 
d  =  6000. 

6000  —  4000  =  2000. 

13.  It  would  increase  the  weight  fourfold  [§  100  (1)]. 
§  107.  See  Daniell's  "  Principles  of  Physics,"  p.  107. 


62  [Elements  of  Natural  Philosophy,  pp.  60-52.] 

§  108.  See  First  Prin.  Nat.  Phil,  Exp.  34  and  Picker, 
ing's  "  Physical  Manipulation,"  p.  66. 

§  111.  See  First  Prin.  Nat.  Phil,  §  68,  a. 

With  the  point  of  a  pen-knife  blade,  make  a  hole  of  2 
or  3  mm.  diameter  in  the  large  end  of  an  egg.  In  the 
small  end,  prick  a  pin-hole.  Blow  the  contents  of  the 
shell  out  through  the  larger  hole.  Rinse  and  dry  the 
shell.  Drop  a  little  pulverized  rosin  or  melted  sealing-wax 
through  the  larger  hole  into  the  smaller  end  of  the  egg. 
Support  the  egg  in  a  small  tin  can  (that  may  be  obtained 
from  any  kitchen)  or  in  any  other  convenient  way,  and 
pour  a  few  grams  of  melted  lead  through  the  larger  hole 
and  into  the  smaller  end.  The  lead  will  not  run  out 
through  the  pin-hole  even  if  the  rosin  or  sealing-wax  be 
not  used.  The  larger  hole  may  be  neatly  concealed  with 
a  piece  of  thin  paper  put  on  with  flour  paste.  You  have 
a  "  magical  egg  "  that  persists  in  standing  on  its  smaller 
end. 

Prepare  an  A-shaped  frame,  like  that  shown  in   the 

figure,  making  the  stick,  B  D, 

jfc^'  2  or  3  feet  long.     Place  the 

■'-^^i,,,,,,,,,,,,,,,,,,, „utl„ir»ll„„l,l„,l„„,u,„„l„iiP     le&  -P*  uPon  a  snelf  or  table, 

-^^^^^Zl^K^^  as  shown,  and  hang  a  pail  of 
JUiM!lll\jlMlffllB|M  ^^^^^  water  or  other  weight  at  E. 

I!    |jyE  The  centre  of  gravity  will  fall 

II  B  below  the  point  of  support  and 

the  frame  and  its  load  will  be 
in  stable  equilibrium.  The  apparatus  may  be  rocked 
up  and  down,  like  the  cavalryman  mentioned  in  the 
text-book.  If  the  weight  be  removed  from  E,  the 
frame  will  fall  to  the  floor.  Instead  of  the  cross-bar 
at  G,  a  stout  cord  or  wire  may  be  used.  You  may  sim- 
plify the  apparatus  (and  thus  increase  the  probability 
of  pupils  trying  the  experiment  at  home)  by  cutting  a 
notch  on  the  under  side  of  the  stick,  B  D,  near  the  end, 


touts  of  WtdurrU  Pid'oHophy,  pp.  :,:->, ,;.\ 


03 


to  receive  the  tapered  end  of  the  stick,  ED.  The  end  at 
E  is  thrust  into  a  pail  of  water.  A  stout  cord  extends 
from  the  handle  of  the  pail  to  a  point  on  B  D,  near  <\  the 
cross-bar  being  wholly  omitted.  The  length  of  this  eon! 
may  be  so  adjusted  that  the  pail  will  he  supported  to 
low  B. 

Exercises,  Paf/e  56. 


1. 

First  answer,    600  lb.      Second  answer,    300  lb. 

2. 

u 

a 

3000  miles.      " 

(C 

2000  miles. 

3. 

a 

a 

200  lb. 

tt 

128  lb. 

4. 

a 

tt 

112J  lb. 

a 

96  1b. 

5. 

a 

a 

3000  miles.      " 

ft 

4000  miles. 

6. 

(1 

a 

1000  lb. 

a 

250  lb. 

7. 

Second 

I" 

200  lb.       First 

a 

120  lb. 

8. 

First 

a 

3500  miles.  Second 

tt 

4000  miles. 

9. 

a 

a 

90  lb. 

tt 

213J  lb. 

10. 

a 

t( 

3200  miles.      " 

tt 

8000  miles. 

11. 

a 

tt 

1500  miles.      " 

tt 

16  lb. 

12. 

tt 

tt 

576  lb. 

it 

20000  miles. 

13. 

Second 

Lw 

1024  lb.       First 

tt 

3000  miles. 

14. 

First 

n 

3750  miles.  Second 

tt 

20000  miles. 

15. 

Second 

a 

13520  lb.       First 

a 

2704  lb. 

§  118.  The  statement  that  "the  force  of  gravity  is  a 
constant  force,"  is  sensibly  true  for  all  attainable  distances 
from  the  surface  of  the  earth.  But  if  we  were  able  to 
drop  a  body  from  a  point  several  hundred  or  thousand 
miles  above  the  surface  of  the  earth,  the  force  of  gravity 
would  sensibly  increase  as  the  body  approached  the  earth. 
(§  100  [2]).  The  velocity  would  not  be  an  uniform^ 
accelerated  velocity. 

^  1 22.  See  Deschanel's  "  Natural  Philosophy,"  §§  34-37. 
^  1M4.  See  Pickering's  "Physical  Manipulation,"  p.  84. 


64  [Elements  of  Natural  Philosophy,  pp.  63-67.1 

§  127.  The  value  of  g  is  computed  by  the  formula 

7T*l 

iu  which  n  represents  the  ratio  of  diameter  to  circumfer- 
ence (3.14159) ;  I,  the  length  of  a  given  pendulum  and  t, 
the  time  (in  seconds)  of  its  single  vibration.  By  measure- 
ment, the  value  of  I  is  determined  (§  142).  By  counting 
the  number  of  vibrations  for,  say  30  minutes,  and  dividing 
the  number  of  seconds  (1800)  by  the  number  of  vibrations 
as  counted,  the  value  of  t  is  determined.  See  Deschanel's 
"  Natural  Philosophy,"  §§  44,  47,  48. 

At  the  earth's  equator,  g  =  9.781  m.  or  32.0902  ft. 
At  the  poles,  g  ==  9.831  m.  or  32.2549  ft.  Hence,  the  force 
of  gravity,  per  gram,  varies  from  978.1  to  983.1  dynes 
(§  69).     In  latitude,  45°,  g  =  9.806  m. 

Exercises,  Page  67 '. 
4.  Answer,  80.4  ft. 

6.  S  =  \gt\ 

S  =  16.08  ft.  x  (i)2  =  16.08  f t.  x  i  =  4.02  ft. 

7.  Substituting  in  the  same  formula, 

8  =  16.08  ft.  x  {li)2  sr  36.18  ft. 

8.  S  =  16.08  ft.  x  (12J)2  =  2512J  ft. 

Note. — Remember  that  the  body  is  supposed  to  be  falling  freely  ; 
the  resistance  of  the  air  is  disregarded. 

9.  S  =  \gt\ 
787.92  =  16.08*2. 

49  =  t\  .-.  7  =  t. 

10.  Answer,  225.12  ft.  (v  =  VfyS     See  §  254.) 

11.  Answer,  498.48  ft. 

12.  6£  oz.  +  6-J-  oz.  -f-  2  oz.  -f  1  oz.  ==  16  oz.,  the  total 
weight  to  be  moved. 

To  move  this  weight,  we  have  the  gravity  of  the  rider,  a 
force  of  1  oz.     This  force  can  give  to  an  ounce  of  matter  a 


[Elements  of  Natural  Philosophy,  p.  67.]  65 

velocity  of  (g  =)  32. 1G  ft.  per  second  ;  the  same  force  can 
give  to  16  oz.  of  matter  only  ^  of  this  velocity. 

32.16  ft -^  16  =  2.01  ft. 

13.  S=igfl.        (See  §136.) 
257.28  =  16.08/2.         /.  /  =  4. 

The  ball  will  reach  the  ground  at  the  end  of  4  seconds. 
During  that  time  it  will  move  from  the  tower  (60  ft  x  4  =) 
240  ft. 

14.  During  4  seconds  it  will  fall  257.28  ft.  During 
6  seconds  it  will  fall  578.88  ft  During  the  5th  and  6th 
seconds  it  will  fall  578.88  ft.  —  257.28  ft  =  321.6  ft.  Or 
we  may  say  that  its  average  velocity  during  these  two 
seconds  will  be  that  attained  at  the  end  of  the  5th  second, 
which  is  160.8  ft.  Moving  at  this  average  rate  for  two 
seconds,  it  will  move  (160.8  ft.  x  2  =)  321.6  ft. 

15.  See  §  132.  It  can  rise  for  2  J  seconds.  At  the  time 
specified  it  will  have  been  falling  \  second,  and  will  have  a 
velocity  of  16.08  ft 

16.  Fl  represents  the  distance  that  gravity  will  move 
the  body  during  the  first  second.  Fa  represents  the 
velocity  due  to  the  horizontal  impelling  force,  or  the  dis- 
tance that  force  would  move  it  in  the  first  second.  Aa 
represents  the  amount  of  deviation  from  a  horizontal 
plane,  as  a  consequence  of  the  pull  of  gravity  during  the 
first  second.  It  is  equal  to  Fl.  Fc  represents  the  hori- 
zontal distance  the  projectile  will  move  in  3  seconds.  It 
is  3  times  the  initial  velocity.  Dd  represents  the  total 
pull  of  gravity  for  four  seconds  from  starting. 

17.  S  =  igP.    (See  §131.) 

S  ss  16.08  ft.  x  16  =  257.28  ft. 

This  is  the  distance  the  body  would  have  moved  in  the 
given  time  if  it  had  had  no  initial  velocity.  But  it  moved 
(357.28-257.28=)   100  ft  further  in  the  4  seconds. 


06  [Elements  of  Natural  Philosophy,  pp.  67,  68.] 

The  initial  velocity  must,  therefore,  have  been  (100  4*4  ±±) 
25  ft. 

18.  During  that  time,  gravity  alone  moved  it  2512.5  ft. 
The  additional  force  moved  it  (35  x  12£  =)  437.5  ft. 
Together  they  moved  it  (2512.5  +  437.5  =)  2950  ft.  Its 
final  velocity  due  to  gravity  is  (32.16  x  12.5  =)  402  ft., 
to  which  we  must  add  the  initial  velocity,  making  a 
velocity  of  437  ft. 

19.  (a.)  3216  -r-  32.16  =  100,  the  number  of  seconds. 
See  §  132. 

(b.)  The  end  of  the  4th  second  of  the  ascent  corresponds 
to  the  end  of  the  96th  second  of  the  descent. 

v  =  gt  =  32.16  ft.  x  96  =  3087.36  ft. 

Do  not  forget  that  this  result  disregards  the  resistance  of 
the  air ;  that  it  is  true  only  for  a  freely  falling  (or  rising) 
body. 

(c.)  The  end  of  the  7th  second  of  the  ascent  corresponds 
to  the  end  of  the  93d  second  of  the  descent, 

v  =  32.16  ft.  x  93  =  2990.88  ft. 

20.  The  ball  has  to  fall  from  a  height  of  257.28  ft. 
Whether  the  force  of  gravity  draws  it  vertically  downward 
as  a  freely  falling  body,  or  acts  with  the  projecting  force 
to  produce  a  curved  path,  it  will  reach  the  ground  in  the 
same  time.  (§  78.)  It  would  fall  this  distance  in  what 
time? 

S  =  igt2;  257.28  =  16.08^;   16  =t*;   ^  —  t. 

If  it  would  take  4  seconds  to  fall  from  the  highest  point 
reached,  it  would  require  4  seconds  for  it  to  rise  to  that 
height;  it  would  be  in  the  air  8  seconds.  (§136.) 
During  each  of  these  seconds  it  has  a  horizontal  motion  of 
1000  ft. 

21.  S=  \gt%  =  16.08  ft.  x  25  =  402  ft.,    the    distance 


[Elements  of  Natural  Philosophy,  pp.  67,  68.]  67 

that  the  force  of  gravity  would  move  the  body  in  5  seconds. 
The  force  with  which  it  was  thrown  moves  it  10  ft.  t-acli 
second,  or  50  ft.  during  the  5  seconds. 

402  ft.  4-  50  ft.  =  452  ft.         (§  131.) 

22.  v  =  gt  =  32.16  f t.  x  5  =  160.8  ft. 

160.8  ft.  +  10  ft.  =  170.8  ft. 

23.  See  §125.  (a.)  The  value  of  each  space  is  7  ft. 
In  5  seconds  it  will  pass  over  (t2  =)  25  such  spaces,  or  175  ft. 

(b.)  Its  final  velocity  will  be  (2*  =)  10  times  7  ft.  =  70 
feet.    See  §  125. 

24.  (a.)  See  §§  124,  125.  The  distance  passed  over  in 
the  first  second  will  be  half  the  velocity  acquired  during 
the  first  second.  Hence,  the  value  of  the  spaces  traversed 
in  this  case  is  10  ft.  In  10  seconds  it  will  pass  over  (t2  =) 
100  such  spaces,  or  1000  ft.  Or  we  may  say  that  the 
increment  of  velocity  (g)  under  these  circumstances  is 
20  ft.,  instead  of  32. 16  ft.     Then, 

S  =  \gt2  =  10  ft.  x  100  =  1000  ft. 

(b.)  See  §130.  The  ratio  between  the  height  and 
length  of  the  plane  is  the  same  as  that  between  20  ft.  and 
32.16  ft. 

20:32.16  ::  800  ft.  :  1286.40  ft. 

25.  See  §  132.  (a.)  It  would  take  just  as  long  to  rise 
1302.48  ft.  as  it  would  to  fall  that  distance.     Then, 

8  as  \gt2 ;    1302.48  sa  16.08/2 ;    81  =  fi ;    9  =  i. 

(b.)  The  initial  velocity  of  a  body  that  can  rise  for 
9  seconds,  is  the  same  as  the  final  velocity  of  a  body  that 
has  fallen  for  9  seconds.    Then, 

v=gt  =  32.16  ft.  x  9  =  289.44  ft. 

26.  During  7  seconds,  gravity  would  give  it  a  velocity  <>f 
(gt  as  32.16  ft.  x  7  =)  225.12  ft.  But  as  its  velocity  is 
235.12  ft, it  must  have  had  an  initial  velocity  of  (235.12  — 


68  [Elements  of  Natural  Philosophy,  pp.  67-73.] 

225.12  =)  10  feet  During  4  seconds,  gravity  would  move 
it  (yt2  =  16.08  ft.  x  16  =)  257.28  ft.  But  during  each 
of  these  4  seconds,  the  force  of  the  throw  moves  it  10  feet 
more.  This  amounts  to  40  additional  feet  during  the 
4  seconds. 

257.28  ft.  +  40  ft.  =  297.28  ft. 

27.     S  =  \g&\  787.92  =  16.08*2;  49  =  P ;  7  =  t 
This  is  the  time  that  the  second  body  was  in  falling 
787.92  ft.     But  the  first  body  fell  3  seconds  more,  or  10 
seconds.     During  10  seconds  it  would  fall  16.08  ft.  x  100  = 
1608  ft. 


[Elements  of  Natural  Philosophy.]  69 

§  146.  See  First  Prin.  Nat.  Phil,  Exp.  39.     Formulas 
f«»r  tli is  law  may  be  given  as  follows: 
I  :  L  =  P  :  T\ 
L:l  =  n*:N*. 
The  Fourth  Law  of  the  pendulum  is  as  follows  :   The 
time  of  vibration  varies  inversely  as  the  square  root  of 


the  accelerating  force,  or  as 


VI- 


§  147.  FoucauWs  Experiment,  in  which  the  persistence 
of  the  pendulum  in  its  plane  of  vibration  is  used  to  prove 
the  rotation  of  the  earth  on  its  axis,  is  described  in  Frick's 
"Physical  Technics,"  p.  143  (§  120).  For  the  use  of  the 
pendulum  to  determine  the  value  of  g,  see  the  Hand-Book 
note  on  §  127.  It  is  interesting  to  notice  that  the  length 
of  the  second's  pendulum  is  very  nearly  a  meter. 

Exercises,  Page  75. 

1.  (b.)  Time  is  3  seconds. 

(a.)  39.1  inches  x  9  =  351.9  inches.     (See  §  146.) 

2.  (b.)  Time  is  2  seconds. 

(a.)  39.1  inches  x  4  =  156.4  inches. 

3.  We  have  two  pendulums  to  compare ;  the  second's 
pendulum,  the  length  and  time  of  which  are  known  (§  147), 
and  the  given  pendulum,  the  length  of  which  is  30  inches, 
but  the  time  of  whose  vibration  we  are  to  find.  From 
§  146,  we  have  the  formula, 

L  :  I  =  T* :  t*. 
Let  the  capital  letters  refer  to  the  second's  pendulum. 
Then  we  may  substitute  as  follows  : 

39.1  :  30  =  1«:  fc     .-.  P  =  0.7672  .-.  t  a=  0.87. 
Since  the  time  of  one  vibration  is  0.87  seconds,  there  will 
be  as  many  vibrations  in  60  seconds  as  .87  is  contained 
times  in  60,  which  is  68.9.     Hence  the  number  per  minute 
is  69  nearly. 

4.  39.1  :  16  =  l2 :  rf2.      .\  t  =  0.64—. 
The  number  of  vibrations  is  93.7 -f-. 


70  [Elements  of  Natural  Philosophy,  p.  75.] 

5.  (b.)  60  -j-  J  =  240,  the  number  of  vibrations  per 
minute. 

(a.)  39.1  :  Z  ::  1>  :  (J)2.  .\  Z  ==  2.44+  inches.  Or  we 
may  say  that,  as  the  time  is  J  that  of  the  second's  pen- 
dulum, the  length  will  be-^  that  of  the  second's  pendulum, 
or  2.44+  inches. 

6.  (b.)  60  sec.  -f- 15  sec.  =  4,  the  number  of  vibrations 
per  minute. 

(a.)  39.1  :  I  ::  l2 :  152.  Or  since  the  time  is  15  times 
that  of  the  second's  pendulum,  the  length  will  be  (152  =) 
225  times  the  length  of  the  second's  pendulum. 

7.  39.1  :  39.37  : :  l2  :  t\     .\  t  =  1  +  seconds. 

Notice  how  closely  the  meter  corresponds  to  the  length 
of  the  second's  pendulum  : 

(39.37  in.  —  39.1  in.  =  0.27  in.) 

8.  (b.)  Time  of  1  vibration  =  6  seconds. 

(a.)  39.1  inches  x  36  =  1407.6  inches  =  117.3  ft. 

9.  39.1  :  10  ::  l2 :  t\         .*.   t  =  ±  +  . 

10.  The  time  =  60  seconds.  The  length  =  39.1  inches 
X  3600  sb  11730  ft.,  or  more  than  2£  miles. 

11.  The  length  of  this  pendulum  is  that  of  the  second's 
pendulum.  Hence  the  number  of  vibrations  is  1  per 
second,  and  the  time  is  1  second. 

(1000  mm.  —  993.3  mm.  =  6.7  mm.) 

12.  (a.)  99.33  cm.  x  ±  =  397.32  cm.  —  3.9732  m. 

13.  (a.)  99.33  cm.  x  1202  =  1430352  cm. 

se  14303.52  m.  =  14.3+  Km. 


[Elements  of  Natural  Philosophy,  p.  75.]  71 

14.  U>.)  99.33:24.83  ::  l2 :  P. 

15.  (b.)  Time  =  -J  second. 

(a.)  Length  =  993.3  trim,  x  (i)2  =  15.52  mm. 

16.  (b.)  99.33  :  397.32  ::  l2 :  Z2.         .\  t  =  2. 

17.  (A.)  99.33  :  11.03  ::  1»:  Z2.        .•.*==$  nearly. 

18.  (a.)  99.33  cm.  x  100  =  9933  cm.  =  99.33  rn. 

19.  (£.)  99.33  :  2483.25  ::  l2 :  Z2.         .\  t  =  5. 

Suggestion. — Divide  the  1st  couplet  by  99.33. 

20.  (a.)  99.33  cm.  x  16  =  1589.28  cm.  =  15.8928  m. 

21.  X:Z  ::  T* :  Z2.        .-.  4:49  ::  T2 : /*. 

/.  2:7  ::  T:  t 

22.  L:l  ::  n*:N*.     (See  §146.) 

.-.  L\l  ::  4900:6400. 

23.  The  time  of  the  longer  pendulum  will  be  twice  that 
of  the  shorter  one. 

24.  39.1  inches  x  (\)2  =  1.564  inches. 

25.  (a.)  39.1  inches  x  64  =  2502.4  inches,  or 

99.33  cm.  x  64  =  6357.12  cm.  =  63.57+  m. 

(b.)  39.1  inches  -=-  64  =  0.61  inches,  or 

993.3  mm.  x  &  =  15.5  mm. 

26.  39.1  in.  x  (3.5)2  =  478.975  in.,  nearly  40  ft. 

27.  Time  of  vibration  =  .8  seconds. 

39.1  in.  x  (0.8)2  =  25.02  +  in. 

28.  L  :  /  : :  n»  :  NK 

:.  60  in. :  60.5  in.  ::  n* :  4002.     .-.  n  =  398  +  . 


72  [Elements  of  Natural  Philosophy,  pp.  78,  79.] 

§  150.  Be  sure  that  your  pupils  understand  that  work  is 
the  product  of  two  factors ;  viz.,  force  and  resistance 
through  space.  If  either  factor  is  zero,  the  product  is 
zero  and  no  work  is  done.  A  planet  or  a  comet  imagined 
as  moving  without  resistance  must  be  conceived  as  doing 
no  work.  Similarly,  a  pillar  supporting  a  weight  does  no 
work. 

§  154.  The  work  of  lifting  1  gram  to  a  height  of  1  cen- 
timeter is  980  ergs.  The  work  of  lifting  a  kilogram  to 
that  height  is  1,000  times  as  great,  or  980,000  ergs.  The 
work  of  lifting  a  kilogram  100  times  as  high  (100  cm.  = 
1  meter)  is  100  times  as  great,  or  98,000,000  ergs.  But 
the  work  of  lifting  a  kilogram  to  a  height  of  a  meter  is  a 
kilogrammeter.  Hence,  a  kilogrammeter  is  equivalent  to 
98,000,000  ergs. 

§  156.  See  First  Prin.  Nat.  Phil,  Exp.  40. 

§  157.  Force  (the  cause  of  motion)  is  properly  meas- 
ured by  the  acceleration  it  produces  in  the  velocity  of  unit 
of  mass.  Thus,  force  and  mass  are  measured  by  each 
Dther.  Two  forces  are  equal  when  they  produce  equal 
accelerations  in  equal  masses ;  two  masses  are  equal  when 
they  are  equally  accelerated  by  equal  forces.  The  velocity 
(v)  is  directly  as  the  force  (/)  and  inversely  as  the  mass 
(m).  When  the  force  is  constant,  velocity  is  proportional 
to  the  time  of  action  (t)  also.     That  is, 

f 
v  =  —  x  t    .'.  mv  =  ft.  (1.) 

The  space  (S)  through  which  a  body  moves  under  the 
action  of  a  constant  force  is  also  directly  as  the  force  and 
inversely  as  the  mass.  But  we  learn  from  §  128  (3),  where 
the  particular  constant  force  is  represented  by  g,  that  the 


[Elements  of  Natural  PhUowphy,  p.  79.]  73 

space  is  proportional,  not  to  the  time  (as  velocity  is ;  v=gt 
but  to  half  the  square  of  the  time  ( S=g  ^  I .     Consequently, 


Substituting  the  value  of  f*  given  in  equation  (2), 

/ 


Multiplying  both  members  of  this  equation  by 

fS=imv>.  (5.) 

But  the  product  of  the  force  acting  and  the  space 
through  which  the  body  is  moved  measures  the  work 
(§  150)  done  on  that  body  and,  consequently,  the  energy 
required  to  do  the  work.  In  other  words,  the  product, 
f  S,  represents  kinetic  energy  and  equation  (5)  becomes 
K.  E.  =  i  mv>. 


74  [Elements  of  Natural  Philosophy.'] 

Exercises,  Page  S3, 

1.  See  §  155. 

tt  _  No.  of  feet  x  No.  of  lbs.  _  Foot-pounds 

orse-powei  —  33000  x  No.  of  minutes  ~      33006~m.~ 

176  x8250      L-V'i;  \        ^ 

-OQQQQ r  =  11*  the  number  of  horse-power. 

Suggestion. — Reduce  by  cancellation. 

o    /a      g  -.  ^  x     192.96  x  10000       lJj^- 

2.  (See§lo7.)    — ^- =  30000. 

3.  The  direction  makes  no  difference  (§  156). 

50  x  19.6  x  19.6       ^       rj. 

2xk8         *  5°  X  19-6  *  980' 

the  number  of  kilogram-meters.     K.  E.  ~  w  ( — ^-1 .    See 

V8.02/ 
page  66,  following. 

4.  See  §132   (a).     Gravity  will  diminish  the  velocity 
32.16  ft.  each  second. 

(a.)    In  3  seconds  it  will  diminish  it  96.48  ft.      The 
velocity  at  the  end  of  3  seconds  will  be 

225.12  ft.  -  96.48  ft.  ==  128.64  ft.     (§  157.) 

K.E.  =  10xlf°j*f8-64  =  2572.8, 

the  number  of  foot-pounds,     (v  =  VfyS.) 

(b.)    v  =  gt  =  32.16  ft.  x  4  =  128.64  ft.     (§  128.) 

The  weight  and  velocity  being  the  same  as  before,  the 
X.  E.  will  be  the  same,  i.  e.,  2572.8  foot-pounds. 

K   40x8£x8J 


2x9.8 


141f£f-,  the  num.  of  kilogram -meters. 


*    /B1KK  x  1500x2376     _  . ,  ,         _. 

6.  (§155.)       0      — —=36,  the  number  of  horse-power 
00UUU  X  o„ 


\EUment%  of  Natural  Philosophy,  p.  83]  75 

7.  That  quantity  of  water  weighs  about  (62.51b.  x  300=) 
18750  pounds. 

62.5x300x132  • 

33000  ~      ' 

the  number  of  horse-power  necessary. 

8.  A  velocity  of  20  miles  per  hour  is  one  of  29 J  ft.  per 
second. 

v  „        100  x  204  x  29^  _        , ,    ,  _ 

K.  E.  = — ^ *  =  number  of  foot-pounds. 

64.32 

9.  (a.)  6000  x  50  =  300000,  the  number  of  foot-pounds. 

(b.)  300000  -r- 16500  =  the  number  of  horse-power. 
(§155.) 

0       10000x100 

10-       *~    teboom   •     •••™  =  15A> 

the  number  of  minutes. 

the  number  of  feet. 

12.  1650000  -r-  33000  ==  50,  the  number  of  horse-power 

2376  x  1000       oa  ,,  ,        _, 

13.  ^/x/v/x -r-  =  36,  the  number  of  horse-power. 

33000  x  2  r 

K.K  =  ^«>  =  1250, 

the  number  of  foot-pounds  that  the  moving  sphere  can 
perform.  This  working  power  is  the  exact  measure  of  the 
work  performed  upon  it.  Hence,  the  answer  is  1250  foot- 
pounds.    (§  162.) 

15.  A  resistance  of  8  pounds  per  ton  signifies  that  to 
move  a  ton  one  foot  on  the  mils  involves  as  much  work  as 
to  lift  8  lbs.  one  foot  high,  or  8  foot-pounds.  To  move 
10  tons  50  feet  on  the  rails  would  require  4000  foot-poum'.-. 
The  additional  work  done  in  giving  kinetic  energy  (or 


/6  [Elements  of  Natural  Philosophy,  pp.  83-85.] 

velocity)  to  the  car  will  be  measured  by  the  kinetic  energy 
of  the  car.     The  velocity  of  the  car  is  4.4  ft.  per  second. 

20000  x  4.4  x  4.4  _ 
KE'- 6452 -6019  +  > 

the  number  of  foot-pounds  that  the  car  can  perform,  or 
the  amount  of  work  done  in  giving  the  car  the  velocity 
specified. 

4000  foot-pounds  +  6019  +  foot-pounds 
=  10019  +  foot-pounds, 

the  whole  amount  of  work  done. 

Heview  Questions,  Page  84* 

4.  (a.)  See  §21. 

8.  (a.)  Gravity  is  a  variety  of  gravitation  ;  the  latter 
includes  the  former  ;  the  latter  is  of  universal  application  ; 
the  former  is  (as  generally  understood)  confined  to  the 
earth  and  bodies  thereon. 

10.  (a.)  See  §  120.  (c.)  Galileo  was  Professor  of  Mathe- 
matics at  the  Universities  of  Pisa  and  Padua,  Italy.  He 
was  born  A.  D.  1564,  and  died  in  1642. 

12.  (/.)  Its  isochronism.  This  property  of  the  pen- 
dulum is  said  to  have  been  discovered  by  Galileo,  by 
observing  the  swinging  of  the  chandelier  in  the  cathedral 
at  Pisa,  in  1582. 

13.  Refer  to  Fig.  9.  In  this  case  the  parallelogram  will 
be  a  rectangle.  Make  AB  =  8  cm.  and  AC  =  6  cm. 
Complete  the  rectangle.  Draw  the  resultant,  AD.  The 
line  AD  is  the  hypothenuse  of  the  right-angled  triangle 
ABD  or  A  CD,  and  its  numerical  value  is  10.  It  therefore 
represents  a  force  of  10  pounds  acting  from  A  toward  D. 
Its  equilibrant  would  be  a  force  of  10  pounds  acting  in  the 
opposite  direction,  or  from  D  toward  A. 

17.  (a.)  To  discover  or  to  illustrate  physical  truths. 


[Elements  of  Natural  Philosophy,  p.  85.]  77 

18.  The  first  ball  has  a  momeDtum  of  300.  (§  70.) 
After  striking  the  secoud  ball,  since  they  are  inelastic 
(§  i>4),  they  will  move  together,  but  the  momentum  will 
be  uuchanged.  Since  the  weight  is  now  12  (=  5  +  7)  and 
the  momentum  is  300,  the  velocity  is  (300  -=-  12  =)  25  feet 
per  second.  After  the  second  impact,  the  momentum  is 
still  300,  but  the  weight  is  (5  +  7  +  8  =)  20  pounds. 
The  common  velocity  will  therefore  be  (300  -r-  20  =)  15 
feet  per  second. 

19.  See  §  68  (a).  32,10  x  9  =  289.44,  the  number  of 
F.  P.  S.  units. 

20.  See  §  69  (a).     9  Kg  =  9,000^. 

980  dynes  x  9000  =  8,820,000  dynes. 

21.  K.  E.  =  \  mv>  =  i  x  50  x  60*=  90,000. 

22.  K.  E.=  i  mv*  =  $  x  30  x  40,0002  =  24,000,000,000= 
24  x  10». 


CHAPTER  III. 

§  163.  "  Any  arrangement  of  the  mechanical  powers  designed  tn 
transmit  work  undiminished  is  called  a  machine.  The  more  nearly 
this  design  is  realized  in  actual  combinations  of  materials,  the  more 
closely  the  machine  approaches  perfection.  The  elasticity  of  the 
materials  we  are  compelled  to  employ,  friction  and  other  causes 
which  modify  the  conditions  required  by  theory,  make  the  attain- 
ment of  such  perfection  impossible.  The  ratio  of  the  useful  work 
done  to  the  energy  expended  is  called  the  efficiency  of  the  machine. 
Since,  in  every  actual  machine,  there  is  a  loss  of  energy  in  the  trans- 
mission, the  efficiency  is  always  a  proper  fraction/' — Anthony  and 
Brackett. 

§  168.  See  Frick's  "  Physical  Technics,"  p.  69. 

§  170.  See  First  Prin.  Nat.  Phil,  Exps.  42,  43. 

§  175.  See  Deschanel's  *  Natural  Philosophy,"  §§  54-57. 

"  In  the  balances  usually  employed  in  physical  and  chemical  in- 
vestigations, various  adjustments  are  provided  by  means  of  which 
all  the  required  conditions  may  be  secured.  The  beam  is  poised  on 
knife  edges  and  the  adjustment  of  the  centre  of  gravity  of  the  beam 
is  made  by  changing  the  position  of  a  nut  which  moves  on  a  screw 
placed  vertically,  directly  above  the  point  of  suspension.  Perfect 
equality  in  the  moments  of  force  due  to  the  two  arms  of  the  beam 
is  secured  by  a  horizontal  screw  and  nut  placed  at  one  end  of  the 
beam.  The  beam  is  a  flat  rhombus  of  brass,  large  portions  of  which 
are  cut  out  so  as  to  make  it  as  light  as  possible.  The  knife  edge 
on  which  the  beam  rests  and  those  upon  which  the  scale-pans  hang 
are  arranged  so  that,  with  a  medium  load,  they  are  all  in  the  same 
line.  A  long  pointer  attached  to  the  beam  moves  before  a  scale  and 
serves  to  indicate  the  deviation  of  the  beam  from  the  position  of 
equilibrium.  If  the  balance  be  accurately  made  and  perfectly  ad- 
justed and  equal  weights  placed  in  the  scale-pans,  the  pointer  will 
remain  at  rest  or  will  oscillate  through  distances,  regularly  di- 
minishing on  each  side  of  the  zero  of  the  scale." — Anthony  and 
Brackett. 


[Elements  of  Natural  Philosophy.] 
Exercise* ,  l*ayv  ft 4. 


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80  [Elements  of  Natural  Philosophy,  p.  95.] 

Page  95. 

21.  §  167  (2).    (a.)  3  feet,     (b.)  10  pounds. 

22.  §  167  (3).     (a.)  8  pounds,     (b.)  5  feet  per  second. 

23.  The  lever  has  equal  arms;  it  is  a  balance  (§175); 
load  =  50  pounds. 

24.  (a.)  15  feet,  (b.)  10  feet,  (c.)  Such  a  lever  can- 
not be  of  the  3d  class,  for  in  such  levers  the  weight-arm  is 
always  greater  than  the  power-arm. 

25.  (a.)  First  and  second  classes,  (b.)  If  of  1st  class, 
30  lb. ;  if  of  2d  class,  40  lb. 

26.  Figure  the  lever.  It  must  be  of  1st  class,  with 
arms  of  4  and  6  feet.     (See  §  172.) 

40  x  4  =  160 ;  1000  x  2  =  2000 ;  160  +  2000  ==  2160, 

the  sum  of  the  moments  for  the  short,  and,  consequently, 
the  moment  of  the  force  to  be  applied  at  the  end  of  the 
long  arm  to  produce  equilibrium.  But  in  the  case  of  the 
long  arm,  6,  the  length  of  the  arm,  is  one  factor  of  this 
2160;  therefore  (2160  -r- 6  =)  360,  the  number  of  pounds, 
is  the  other  factor.     Or,  more  briefly, 

6x  =  2160.         .*.  x  =  360. 

27.  The  lever  is  of  the  first  kind,  with  arms  of  8  and  12 
feet  respectively.  Figure  the  lever.  Kepresent  the  force 
at  the  end  of  the  short  arm  by  x.  Then  will  the  force  at 
the  end  of  the  other  arm  be  represented  by  1200  —  x. 
Placing  the  moments  of  the  two  forces  equal  to  each  other, 
we  have, 

Sx  =  12  (1200  -x)  =  14400  -  12z. 

.-.    20z  =  14400;  x  =  720;  1200  -  x  =  480. 

Answer.  720  lb.  at  the  end  of  the  short  arm,  and 
480  lb.  at  the  end  of  the  long  arm. 

Proof  i  m  +  480  =  130°- 

J'   (720  x      8=    480  x  12. 


[Elements  of  Kaiurat  Philosophy,  p.  .95.  J  &t 

28.  Figure  the  lever,  with  the  first  three  forces  acting. 


40 
300 


100 


340  =  100  +  240. 

We  thus  see  that  an  additional  moment  of  240  is 
needed  with  the  100,  to  produce  equilibrium.  Of  this 
240,  one  factor  is  80  ;  then  the  other  factor  is  3,  the  num- 
ber of  feet  from  the  fulcrum,  on  the  same  side  as  the 
force  of  100  lb.  Or  we  may  represent  the  four  forces  acting 
upon  the  lever,  calling  the  distance  of  the  fourth  from  the 
fulcrum,  x.     Then  we  shall  have 


40 
300 


100 

80s 


340  as  100  +  80s.        .%  x  =  3. 

Suggestion. — In  a  case  like  this,  simple  inspection  will  gen- 
erally show  on  which  arm  to  figure  the  fourth  force  as  acting.  Ii 
it  be  erroneously  represented,  either  as  to  position  or  direction,  the 
result  will  be  a  negative  quantity.  For  instance,  suppose  that  in 
this  case  we  represent  the  force  of  80  lb.  to  be  acting  on  the  same 
arm  as  the  forces  of  10  and  of  100  lb.,  and  in  a  downward  direction. 
We  should  then  have 


40 
300 
80* 


100 


340  +  80^  =  100.  .-.  80r  =  -  240,      or      x=—3. 

Here  the  3  would  indicate  that  the  force  was  acting  at  a  distance  of 
3  ft.  from  the  fulcrum  ;  the  minus  sign  would  indicate  that  the 
force  was  tending  to  turn  the  lever  in  a  direction  opposite  to  that 
assumed.  This  contrary  tendency  might  result  from  an  upward 
force  of  80  lb.  acting  3  ft.  from  the  fulcrum  and  on  the  same  arm 
as  the  10  lb.,  or  from  a  dovmitard  force  of  80  lb.  acting  8  ft.  from 
the  fulcrum  and  on  the  same  arm  as  the  100  lb.  Due  regard  to  the 
algebraic  sign  of  the  result  will  correct  any  error  of  this  kind.  In 
this  problem,  a  downward  force  is  specified  ;  the  problem  is  there- 
fore definite. 


82  [Elements  of  Natural  Philosophy,  p.  96.] 

29.  Draw  a  line,  ab,  to  represent,  on  any  convenient 
scale,  as  1  inch  to  the  foot,  a  lever  6 J  feet  long.  Then 
this  line  will  be  6{  inches  loog.  Measure  on  the  line  j  of 
an  inch  from  b,  for  the  position  of  the  fulcrum  c.  The 
lever  is  evidently  of  the  1st  class,  with  arms  of  5-$-  ft.  and 
|  ft.  respectively.  Represent  a  downward  force  of  60  lb. 
at  a  (Fig.  40).  Locate  d,  2f  inches  (feet)  from  c.  Repre- 
sent a  downward  force  of  75  lb.  acting  at  d.  Represent  a 
downward  force  of  x  pounds  at  b. 


5£  x  60  =  330 
2J  x  75  =  206J 


ix 


536J  =  ix.        .\  x  =  715. 

30.  Figure  the  lever.  Place  the  moments  tending  to 
move  a  upward  in  one  column,  and  those  tending  \o  move 
ic  downward  in  the  other  column. 


40  x  10  =  400 

28:z 


364  =  56  x  6J 
288  =  96  x  3 


28z  +  400  =  652 

28z  =  252 
x=      9 

The  force  of  28  lb.  must  act  at  a  distance  of  9  ft.  from 
the  fulcrum.  It  must  therefore  act  on  the  long  arm,  as 
the  short  arm  is  only  3  ft.  long.  We  assumed  that  the 
force  would  tend  to  draw  a  downward.  This  assumption 
was  not  contradicted  by  a  negative  result.  The  force  will 
therefore  act  downward,  at  a  distance  of  1  ft.  from  a. 

31.  Draw  a  line  18  cm.  long  to  represent  the  beam. 
(Scale :  1  cm.  =  1  ft.)  Letter  its  extremities  a  and  b. 
At  a  point  3  cm.  from  a,  represent  a  downward  force  of 
2,000  lb.  At  a  point  8  cm.  from  b,  represent  a  downward 
force  of  1,400  lb.  (See  §174.)  Consider  either  end  as 
the  power. 


[Elements  of  Natural  Philosophy,  pp.  95,  96. 

Power  at  ft. 

2000  x     3  =    C000 
1400  v  10  =  14000 

i&k, 

20000 
1111* 

=  18z 

=        X 

83 


Pressure  at  b  =  11 11 J  lb. 

a  ss  (3400  —  1111*  =)  2288J  lb. 


Power  at  a. 
18z 


11200  =  1400  x    8 
30000  =  2000  x  15 


18s  =  41200 
*=    2288| 

Pressure  at  a  =  2288$  lb. 

b  =  (3400  —  2288f  =)  1111*  lb. 

32.  Represent  the  power-arm  by  x  and  the  weight-arm 
by  3  —  x.  Call  40  the  power  and  200  the  weight.  (See 
§170.) 

P:W  ::  WF:  PF,    or    40  :  200  ::  3  —  x  :  x. 

.-.  40z  =s  GOO  —  200z ;    240a;  =  600 ; 
z  =  2|;    3—  x  =  ± 

The  fulcrum  must  be  2 J  ft.  from  the  40  lb.  and  6  inches 
from  the  200  lb. 

Or  we  may  proceed  as  follows  :    The  weight  is  5  times 

power  ;  consequently,  the  power-arm  must  be  5  tunes 

llic  weight-arm.     Dividing  3G  inches,  the  length  of  the 

lever,  into  two  parts,  so  that  one  s'nall  be  5  times  as  great 

as  the  other,  we  have  30  inches  and  G  inches. 


84  [Elements  of  Natural  Philosophy,  p.  96.] 

33.  See  §  176.  Represent  the  true  weight  by  x,  and 
remember  that  1  lb.  9  oz.  =  25  oz.,  and  that  2  lb.  4  oz.  = 
36  oz. 

25  :  x  : :  x  :  36 ;    x*  =  900 ;    a  =  30. 

The  true  weight  is  30  oz.,  or  1  lb.  14  oz. 

34.  See  §174.  A  ought  to  carry  200  1b.;  B,  100  1b. 
Call  the  6  ft.  bar  a  lever  of  the  second  class,  fulcrum  at 
either  end,  as  A's  end.  Then  the  weight  is  300  lb. ;  the 
power,  100  lb.;  the  power-arm,  6  ft.;  the  weight-arm  =  x. 

P:W::WF:PF;    100  :  300  ::  x  :  6; 
300z  =  600 ;     x  =  2. 

The  weight  should  be  hung  2  ft.  from  the  fulcrum,  or  two 
feet  from  A  and  four  feet  from  B. 

35.  As  the  beef  weighs  450  pounds,  A  should  carry  250 
pounds,  and  B,  200  pounds.  Suppose  B  to  act  as  fulcrum 
and  A  as  power. 

P:  W  ::  WF :  PF;    250:450  ::  x  .S; 
9x  =  40  ;    x  =  4$ . 

The  beef  should  hang  4$  ft.  from  the  fulcrum,  or  4$  ft. 
from  B  and  3|  ft.  from  A. 

36.  The  lever  is  of  the  1st  class,  with  arms  of  3^  ft. 
and  (16  —  3i|  =)  12£  ft.  respectively. 

100  x  12J  =  1250  =  Six ;        ,\    x  =z  357}. 

It  would  require  a  power  of  357}  pounds  to  balance  the 
100  pounds.  On  the  supposition  that  the  machine  is  free 
from  friction  and  other  hindrances  to  motion,  anything 
more  than  357}  lb.  would  move  the  load.  In  practice,  m 
allowance,  determined  by  experience,  is  made  for  thes^ 
necessary  hindrances. 


[Elements  of  Natural  Philosophy,  p.  96.]  85 

37.  (a.) 

GO  2 

(J.)  50  x  40  x  33  =  x  x  6  x  5.  .%  2s  2200,  the  number 
of  pounds. 

(c.)  a:  x  40  x  33  =  4400  x  6  x  5.  .-.  a;  =  100,  the  num- 
ber of  Kg. 

Suggestion.— Theoretically,  the  parts  of  a  lever  or  other  simple 
machine  have  no  weight,  suffer  no  loss  by  friction  (§  212),  from  the 
stiffness  of  ropes  (§  192),  the  resistance  of  the  air.  or  similar  causes. 
In  practical  mechanics  these  have  to  be  taken  into  consideration. 
Hence,  the  last  remark  in  §  165  and  the  third  sentence  in  the  Note 
following  §  170. 

See  Frick's  "  Physical  Technics,"  pages  58  et  seq. 


[Elements  of  Natural  Philosophy.] 


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11.  78.74  inches  =  2  meters  =  200  cm.  The  circum- 
ference of  the  wheel  being  20  times  that  of  the  axle,  the 
weight  supported  will  be  20  times  the  power  employed ; 
20  times  13  oz.  =  260  oz.  ==  16 J  lb.     Or  (§  182), 

P  :  W  ::  c  :  O.     Then,  13  :  i  ::  10  :  200.      .-.  x  =  260. 

12.  P  :  W  : :  d  :  Z) ;   a? :  180  : :  6  :  36.       .-.  $  =  30. 
Any  power  greater  than  30  lb.  wTill  move  the  rudder. 

13.  (§  182.)     x  :  2000  : :  8  :  80.         .'.  x  =  200. 

200  -7-  4  =  50.        Ans.  50+  lb. 


[Elements  of  Natural  Philosophy,  p.  102.]  87 

14.  See  Fig.  49.     P:W::d:D;    x  :  1100  ::  1  :  10. 
.-.  x  =  110 ;   110  -j-  4  =  37f        Ans.  2<i  +  lb. 

'  15.  The  circumference  of  the  axle  is  \  of  the  circum- 
ference of  the  wheel ;  \  of  85  lb.  is  14|  lb.    Ans.  14|  +  lb. 

10.  (§  182.)     70  :  300  : :  x  :  120.         . .  x  =  28. 

Or,  the  power  is  ^\  of  the  weight ;  hence,  the  diameter  of 
the  axle  must  be  ^\  of  120  inches  =  28  inches. 

17.  The  diameter  of  the  circle  described  by  the  power 
is  36  inches. 

(<(.)  x  :  62.5  : :  10  :  36.        .-.  x  =  17.36  +  . 

Ans.  17.36+  lb. 
(£•)    (§§  29,  36.)      x  :  20  ::  10  :  36.      .*.    x  =  5.55,  the 
number  of  Kg.  Ans.  5555.5+  grams. 

18.  We  have  two  sets  of  two  men  each.  The  first  set 
move  in  a  circle  14  feet  in  diameter;  the  second  set  in  a 
circle  10  feet  in  diameter.     Find  the  effect  produced  by 


•ach  set  an 

d  add. 

1st  set  - 

-  -  60: 

:  x 

::  14 

2d  set  - 

-  -  80; 

:  x 

::  14 

12  x  14.  .-.  x  =  720 
12  x  10.  /.  x  =  685| 
Total  effect  =  1405  lb. 
19.  The  diameter  of  the  circle  traversed  by  the  horse  is 
14  ft.  The  diameter  of  the  capstan  barrel  is  14  inches ; 
i.e.,  the  first  diameter  is  12  times  the  second  diameter. 
Hence  (§  182),  the  circumference  of  the  circle  traversed 
by  the  horse  is  12  times  as  great  as  the  circumference  of 
the  barrel  of  the  capstan.  From  this  it  follows  that  the 
horse  must  move  12  times  as  far  as  the  house.  (This  may 
be  made  clear  by  computing  the  two  circumferences  ; 
(Hie  of  them  will  show  the  distance  the  horse  travel-  in 
turning  the  barrel  around  once  ;  the  other  will  show  how 
much  rope  was  wound  up,  or  how  far  the  house  moved  for 
tint  revolution  of  the  capstan  barrel.)  Then  the  horse 
must  travel  (5  miles  x  12  =)  60  miles.  At  the  given  rate 
this  will  require  (60  -r-  2 J  =)  24  hours. 

§  200.  See  Frick's  "  Physical  Technics,"  p.  62. 


88 


[Elements  of  Natural  Philosophy.] 
Exercises,  Page  107. 


No. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Power. 

Weight. 

Pullet. 

Inclined  Plane. 

Cords. 

Height. 

Length. 

Base. 

Case. 

251b. 

13  Kg. 

12  oz. 
250  g. 
50  lb. 
15  cwt. 
20  g. 
mo  Kg. 
60  lb. 
751b. 

50  lb. 

IS  Kg. 
96  oz. 

2  Kg. 
3501b. 

3T. 

lHg. 
4000  Kg. 
5401b. 
1001b. 

2 
6 
8 
8 
7 
4 
5 
8 
9 

3  ft. 

2  m. 

3  in. 
1  dm. 
7  ft. 
4rd. 

2m. 

3  m. 

39.37  in. 

3  yd. 

6  ft. 

12  m. 

8  dm. 

2  ft. 
49  ft. 
10  m. 

4tjd. 

1 
1 
2 
1 
2 
1 
2 
1 
1 
2 

16  rd. 

24  m. 
9  m. 
5  yd. 

! 

Suggestion.— In  No.  10,  find  the  base,  and  then  find  the  length, 

11.  Ans.  50  1b.     (§193.) 

12.  Ans.   25  lb.  (§  194),  or  16|  lb.  (§  197). 

13.  Ans.  75  lb.  x  7  =  525  lb.     (§  197.) 

14.  2000  -r-  10  =  200.     Ans.  200+  lb. 

15.  2000  -v-  11  =  181^.     Ans.  181^+  lb. 

16.  There  may  be  12  cords  or  13  cords.  The  friction 
will  support  J  of  the  weight,  leaving  1350  lb.  to  be  other- 
wise supported.  1350  lb.  -f-  13  =  103^  lb.  The  power 
will  move  13  times  as  fast  as  the  weight.  In  another  sense, 
the  velocities  are  equal,  since  0  =  0. 

17.  [For  solution  see  figure  on  page  32.] 

18.  Make  the  construction  very  carefully;  the  larger 
the  figure,  the  better.  Make  the  line  AB  at  least  20  cm. 
long,  and  AC  4  cm.  long.  Notice  that  the  only  object  of 
this  is  to  find  the  position  of  the  plane  with  reference  to 
the  horizon  (i.e.,  the  angle  B).     It  makes  no  difference 


[Elements  of  Natural  Philosophy,  p.  108.]  89 

whether  BC  is  a  dm.  or  a  Km.  long.  Anywhere  on  BC, 
take  the  point  W  to  represent  the  position  of  the  globe. 
Represent  the  gravity  of  the  globe  by  a  vertical  line.  If 
you  adopt  the  scale  of  1  mm.  =  2  Kg.,  this  line  WG  will 
be  12.5  cm.  long.  From  W,  draw  WX,  so  that  it  shall  make 
an  angle  of  45°  with  AB.  This  may  be  done  by  taking 
oi  =  o  W,  and  drawing  a  line  from  W  through  i.  From 
W,  draw  WZ  perpendicular  to  BC.     From  G,  draw  GP 


18. 


parallel  to  WZ,  and  GE  parallel  to  WP.  WE  represents 
the  pressure  of  the  globe  upon  the  plane,  and  WP  the 
tendency  to  move  in  the  direction  WX.  This  tendency 
must  be  resisted  by  the  supporting  force  which  equals  it 
in  intensity  and  is  opposite  to  it  in  direction.  PW  will 
measure  30-}-  mm.,  and  consequently  represent  a  force  of 
60 -f  Kg. 

19.  Draw  ABC,  WG  and  WZ,  as  in  the  last  problem. 
From  }\\  draw  WX  perpendicular  to  WX.  From  G,  draw 
a  line  parallel  to  WZ,  and  prolong  it  until  it  intersects  WXX 


90  [EkmeiUs  of  Natural  Philosophy,  p.  108.] 

at  P .  Complete  the  parallelogram  (if  you  want  to  do  so) 
by  drawing  GE'  parallel  to  WP'.  Measure  GP',  and  find 
its  value  according  to  the  scale  adopted. 

Suggestion. — In  the  18th  problem,  the  supporting  force  tends 
to  lift  the  globe  from  the  plane,  and  thus  make  its  pressure  on  the 
plane  less  than  its  weight ;  in  the  19th,  the  supporting  force  tends  to 
press  the  globe  against  the  plane,  and  thus  make  its  pressure  on  the 
plane  greater  than  its  weight. 


4000  lb.  x  A  =  1200  lb.,  or  P  :  W  : :  h  :  b. 
P:4000  ::  3:10.         .\  P  =  1200. 


21.  (a.)  If  the  power  acts  horizontally, 

50  lb.  x  y  =  125  lb.     Ans.  Nearly  125  lb. 

(b.)  If  the  power  acts  in  the  direction  of  the  incline, 
first  find  the  length  of  the  incline. 

Vl02  +  42  =  10.77+.. 
Then, 

P  :  W  : :  h  :  I        .:   W=  nearly  134.625  lb. 

22.  i  of  40  lb.  is  5  lb. 

23.  The  power  is  (-^-  =)  -^  of  the  weight.  Conse- 
quently, the  base  is  32  times  as  long  as  the  height,  or 
256  ft.  The  length  is  the  hypothenuse  of  a  right-angled 
triangle,  having  sides  of  8  and  256  ft.  respectively. 

A/82  +  2562  =  256.1. 

Suggestion. — If  you  have  pupils  in  the  class  who  can  do  original 
work,  let  them  try  to  solve  the  problem  by  construction.  From  a 
point,  as  W  (see  figure  for  18th  problem,  above),  let  fall  a  line  800 
(or  32)  units  long,  to  represent  the  gravity.  From  W,  draw  a  hori- 
zontal line,  25  (or  1)  units  long,  to  represent  the  supporting  force. 
Join  the  free  ends  of  these  lines,  forming  the  triangle  PWG,  right- 
angled  at  W.  Through  W,  draw  BG,  perpendicular  to  PG.  BG 
represents  the  position  or  direction  of  the  plane.  From  any  point 
in  BG,  as  C,  draw  a  vertical  line  GA,  8  units  long.  From  A,  draw 
AB,  parallel  to  WP,  or  perpendicular  to  GA  and  WG.     From  the 


[Elements  of  Natural  Philosophy,  pp.  108-11?.]  91 

point  where  the  horizontal  line,  drawn  from  A,  intersects  the 
oblique  line,  drawn  through  W,  measure  BC,  and  determine  its 
length  according  to  the  scale  adopted  for  CA.  It  may  make  the 
matter  clearer  to  complete  the  parallelogram,  by  drawing,  from  O, 
a  line  parallel  to  PW,  and  one  from  W  parallel  to  PO.  If  the 
minuteness  of  the  angles  at  O  and  B  is  troublesome,  apply  thf 
same  process  to  other  problems  where  the  ratio  between  power  and 
weight  is  greater  than  fa 

U.  75  lb.  :  4000  lb.  : :  3  ft.  :  160  ft. 

25.  P  :  W  ::  h  :  1;    250  :  1500  ::  5  :  I        /.  I  =  30. 

The  plane  must  be  5  ft.  high,  and  a  little  more  than  30  ft 
iong. 

§  208.  See  First  Prin.  Nat.  Phil,  §  138  (b)  and  (c) ; 
also  Frick's  "  Physical  Technics,"  p.  64. 

§  211.  See  Frick's  "  Physical  Technics,"  p.  73. 

§  214.  See  First  Prin.  Nat.  Phil,  §  144 ;  Frick's 
"  Physical  Technics,"  p.  153  (§  124). 


[Elements  of  Natural  Philosophy.'] 
Exercises,  Page  113. 


No. 

P. 

W. 

c. 

d. 

1 

15  1b. 

GOO  lb. 

10  in. 

iin. 

2 

5  Kg. 

4000  Kg. 

8  m. 

1  cm. 

3 

lib. 

300  lb. 

75  in. 

iin. 

4 

4  lb. 

4801b. 

15  in. 

iin. 

5 

201b. 

8001b. 

20  in. 

i  in. 

6 

25  1b. 

9001b. 

3  ft. 

Iin. 

7 

2  1b. 

192  lb. 

4  ft. 

H  in. 

8 

10  Kg. 

2500  Kg. 

2.5  m. 

1  cm. 

9 

4  oz. 

61b. 

14  ft. 

7  in. 

10 

200  lb. 

7874  lb. 

1  m. 

Iin. 

11 

3  Kg. 

S00  Kg. 

20  cm. 

2  mm. 

12 

3oz. 

864  oz. 

24  ft. 

Iin. 

13 

1001b. 

8  tons. 

10  ft. 

fin. 

14 

100  lb. 

12  tons. 

10  ft. 

|in. 

15.  8  ft.  =  96  inches.  96  inches  -r-  i  inches  =  288. 
The  power  moves  96  inches  while  the  weight  moves  £  inch, 
or  it  moves  288  times  as  fast.  Hence,  the  theoretical 
pressure  will  be  288  times  15  lb.  or  4320  lb.  Deducting 
for  friction,  we  have,  4320  lb.  —  240  lb.  =  4080  lb.,  the 
actual  pressure. 

16.  Diameter  =  16  inches;  circumference  ==  16  inches 
X  3.1416  —  50.2656  inches.     (See  Appendix  A.) 


50  1b.  x  50.2656  x  11 
For  friction,  deduc'  £  of  this, 
Available  power    -    -    -    - 


27646.08  lb. 

3455  76  lb. 

24190.32  1b. 


Any  resistance  less  than  24190.32  lb.  may  be  overcome. 
The  friction  may  be  provided  for  by  deducting  \  of  the 
50  lb.  before  multiplying  by  50.2656  x  11. 


[Elements  of  Natural  Philosophy,  p.  U4.]  93 

Or  (§  167  [2]), 

501b.  x  50.2656  =  WxfT.     .'.    W=  27646.081b. 

Suggestion. — The  distances  here  used  are  those  traversed  dur 
ing  one  revolution  of  the  screw. 


IT.     J>:W::d:C;    P  :  W  ::  1}  :  12  x9  x  3.1416. 
Dividing  the  second  couplet  by  1}, 

P:  W  ::  1:271.4  + 

18.  1  -r-  i  =  8.       15  lb.  x  8  =  120  lb.  Arts. 

19.  The  power  being  given,  it  is  more  convenient  to 
begin  with  the  power.     (See  §  182.) 

P:W::  r:  R.         25  :  W  : :  4  J  :  30.       .-.    W=  166}. 

The  boy  could  support  a  load  of  166|  lb.  with  the  wheel 
and  axle,  without  the  aid  of  the  inclined  plane.  With  the 
inclined  plane,  he  could  support  20  times  as  great  a  load, 
or  33334  lb.     He  could  lift  anything  less  than  3333|  lb. 

20.  (§  167  [2].)  The  threads  of  the  screw  being  an 
inch  apart,  the  teeth  on  the  wheel  must  be  an  inch  apart, 
i.  e.y  the  wheel  must  have  60  teeth. 

25  lb.  x  72  x  60  =  W  x  10.     .\    W  =  10800  lb. 

(This  computation,  so  far,  considers  only  the  endless 
screw  in  action  while  its  axle  turns  around  once.)  The 
jx»wer  at  the  crank  produces  a  tension  of  10800  lb.  on  the 
rope  of  the  pulleys.  Supposing  that  there  are  6  cords  to 
the  pulley  (S  197),  the  pullev  would  exert  a  power  of 
(10800  lb.  x  6  =)  64800  lb.  on  the  wheel  and  axle.  The 
wheel  and  axle  increases  this  intensity  of  power  eight-fold, 
making  it  518400  lb.  Deduct  J  of  this  for  loss  by  friction, 
and  we  have  345600  lb.  for  the  answer. 

%h  (§  167  [2].)     75  x  120  x  81  =  18  W.    /.  W  =  40500. 


94  [Elements  of  Natural  Philosophy,  pp.  114,  115.] 


^  500  1b.  x  7x3x12x6  _   45818181b_ 

Deducting  J  of  this  for  loss  by 

friction 11454.541b. 

We  have,  for  the  force  exerted  ~  34363.64  lb. 


Exercises,  Page  115. 

2.  (c.)  See  §§  171,  181.     P  x  R  =  Wx  r. 

3.  (b.)  See  Fig.  41. 

4.  Second  class ;  the  power-arm  is  the  whole  length  of 
the  lever. 

5.  The  compound  lever.     See  §§  178,  181, 185,  186. 

6.  Same  amount  of  work.  When  the  inclined  plane  is 
used  (h  =  4,  I  =  12),  only  %  as  great  a  power  is  needed, 
but  the  power  has  to  move  3  times  as  far.     (§  152.) 

7.  (c.)  See  problem  17,  p.  108. 

8.  (a.)  Fasten  one  end  of  the  cord  to  the  movable 
block ;  the  cord  will  be  divided  into  9  parts  by  the  mov- 
able pulleys. 

(b.)  See  §  167  (2).  Consider  the  distances  described  by 
the  power  and  weight  respectively  while  the  screw  turns 
around  once.    Then 

Px  C=  Wxd.        .'.  P:W  ::  d :  C. 

See  §  167  (3).     Suppose  that  the  screw  turns  around  once 
in  a  second.     Then 

P  x  C=  Wx  d,        .\  P:W::  d:C. 

9.  (a.)  Loss  of  power,  (b.)  The  fibres  of  the  rope  are 
thus  held  together  ;  were  it  not  for  friction,  the  rope  would 
fall  to  pieces  of  its  own  weight. 

12.  (a.)  20  foot-pounds.     (§  164.)  (b.)  5  ft. 


[Elements  of  Natural  Philosophy,  p.  115.]  95 

13.  See  §  201. 

14  (<t.)  Enough  to  lift  the  body  a  distance  equal  to  the 
difference  between  the  distance  that  the  centre  of  gravity 
is  above  the  base,  and  the  distance  that  it  is  from  the  edge 
over  which  it  is  to  be  turned ;  e.  g.,  in  Fig.  24,  enough 
force  must  be  used  to  perform  the  work  of  lifting  the 
brick  the  distance  (gc  —  qa  =)  nc. 

(b.)  The  first  force  is  instantaneous  or  momentary;  the 
second  is  continued.    (§  118.) 

(r.)  From  paper,  cut  a  right-angled  triangle  with  a 
height  of  10  or  12  cm.  and  a  length  of  about  30  cm. 
Place  the  short  edge  of  the  triangle  along  the  side  of  a 
lead-pencil,  and  wind  the  paper  upon  the  pencil  The 
length  of  the  inclined  plane  becomes  the  thread  of  the 
screw.  In  the  case  of  the  screw,  considered  as  an  inclined 
plane,  the  power  acts  parallel  to  the  base.     (§  203.) 

Suggestion. — It  may  be  well,  from  this  time  to  the  end  of  the 
y.>ar  to  require  daily  of  each  pupil  written  solutions  of  three  or  four 
problems  as  review  work.  For  instance,  tell  the  class,  on  Friday,  to 
bring  to  the  recitation  on  Monday,  solutions  (written  in  ink  and 
neatly  arranged)  of  the  following  problems:  2d  on  p.  14;  1st  on 
p.  44  ;  1st  on  p.  56.  On  Monday,  tell  them  to  bring  to  the  recitation 
oi  Tuesday  solutions  of  the  following  problems  •  3d  on  p.  44  ;  10th 
on  p.  67  ;  1st  and  2d  on  p.  75.  To  indicate  (not  to  correct)  every  error 
of  any  kind  on  all  of  these  papers  will  require  patient  work  on  the 
part  of  the  teacher,  but  if  the  time  can  be  secured,  its  investment 
here  will  pay.  Papers  notably  poor  should  be  rewritten  until  they 
are  satisfactory.  Pupils  can  soon  be  made  to  see  that  it  is  economy 
to  do  the  work  well  the  first  time— a  vei'y  important  lessen.  Needed 
drill  in  penmanship,  orthography,  syntax,  rhetoric,  and  physics  is 
thus  provided  Any  newspaper  editor  can  testify  that  but  very  feu 
adults  can  prepare  an  article  for  publication  so  that  its  literal  ren- 
Aering  in  print  would  not  bring  a  blush  to  the  cheek  of  the  author. 


CHAPTER    IV. 


§  216.  The  "  Cartesian  Diver,"  a  pretty  piece  of  appa- 
ratus, is  represented  in  the  accompanying  cut.  It  consists 
of  a  figure  suspended  from  a  hollow  glass 
globe  or  balloon,  which  has  a  small  opening 
m  its  lower  part.  The  tall  glass  vessel  is 
nearly  filled  with  water,  in  which  is  floated 
the  figure.  In  trying  the  experiment,  be 
sure  that  the  figure  will  just  float,  L  e.,  that 
the  weight  of  the  figure  with  its  balloon  and 
the  contents  of  the  balloon  is  a  little  less  than 
that  of  an  equal  bulk  of  water.  If  the  appa- 
ratus be  too  light,  warm  the  balloon  gently 
to  expel  part  of  the  air  therefrom,  and,  while 
yet  warm,  immerse  it  in  water.  Water  will 
thus  be  forced  into  the  balloon  and  increase 
the  weight  of  the  apparatus.  If  this  first 
attempt  render  the  apparatus  too  heavy,  hold 
it  so  that  the  contained  water  rests  over  the 
opening  in  the  balloon ;  then  warm  the  bal- 
loon gently,  until  a  drop  or  two  of  water  is  driven  out. 
If  the  first  attempt  did  not  render  the  apparatus  heavy 
enough,  hold  it  so  that  the  water  already  forced  in  will  be 
under  the  opening  instead  of  over  it,  heat  gently,  and 
immerse  as  before.  The  beauty  of  the  experiment  depends 
largely  upon  the  nicety  with  which  the  weight  of  the 
apparatus  is  adjusted.  The  top  of  the  vessel  is  then  closed 
by  snugly  tying  over  it  a  piece  of  elastic  rubber  cloth. 
When  the  finger  is  pressed  upon  the  cloth,  the  air-space 
at  the  top  of  the  jar  is  diminished,  the  tension  of  the  air 
there  is  increased,  the  increased  pressure  thus  exerted  upon 
the  surface  of  the  water  is  transmitted  by  the  water  to  the 
air  in  the  balloon,  the  air  space  in  the  balloon  is  thus 
reduced,  more  water  enters  and  thus  increases  the  weight 
of  the  apparatus,  rendering  its  specific  gravity  greater  than 


[Elements  of  Natural  Philosophy,  p.  I  Hi]  97 

that  of  water.  The  figure  thru  rink*  When  the  finger  is 
removed,  the  tension  of  the  air  in  the  balloon  being  greater 
than  that  of  the  air  at  the  top  of  the  jar,  expels  a  part  of 
the  water  from  the  balloon.  This  reduces  the  specific 
gravity  of  the  apparatus  below  that  of  the  water.  The 
figure  then  risen.  A  pleasing  alternation  of  sinking  and 
rising  may  thus  be  produced.  The  experiment  illustrates 
Pascal's  (§  217)  and  Mariotte's  (§  284)  Laws  and  Ar- 
chimedes' Principle  (§  238).  The  figures  are  often  given 
fantastic  shapes  and  called  "Bottle  Imps."  A  small 
inverted  "  test-tube  "  or  vial  carrying  a  proper  weight  sus- 
pended from  its  mouth  answers  well  for  the  experiment 
Lead  the  pupils  by  questions  to  see  that  when  the  finger  is 
removed  from  the  cloth,  the  tension  of  the  air  in  the  bal- 
xoon  and  in  the  jar  is  equal  to  the  atmospheric  pressure: 
that  when  the  finder  is  pressed  down,  the  tension  of  the  air 
in  the  balloon  and  in  the  jar  is  greacer  than  the  atmos- 
pheric pressure.  The  jar  may  be  closed  with  a  piece  of 
bladder  instead  of  sheet  rubber.  A  common  fruit  jar 
may  be  used  with  a  syringe  bulb  attached  by  a  short  tube 
to  the  perforated  cover  of  the  jar.  Squeezing  the  bulb, 
increases  the  pressure  on  the  surface  of  the  water  in  the 
jar  and  causes  the  image  to  descend. 

A  glass  bulb  about  2  cm.  in  diameter  with  a  little  tube 
ending  with  a  tine  aperture  gives  a  better  illustration  than 
the  more  elaborate  figures  made  of  opaque  and  colored 
glass.  On  the  whole,  it  is  well  to  interest  (and  perhaps 
mystify)  the  class  with  the  colored  images  first  and  thin 
to  use  the  inverted  test  tube  for  observation  and  explana- 
tion. The  images  do  not  cost  much,  and  may  be  had  of 
Jas.  W.  Queen  &  Co.,  924  Chestnut  St.,  Philadelphia. 


98  [Elements  of  Natural  Philosophy,  pp.  123-127.] 

Exercises,  Page  123* 

§  225.  (a.)  Into  a  £7"  tube  pour  enough  mercury  to  fill  each  arm  tc 
the  depth  of  3  or  4  cm.  Place  the  U  tuba  upon  a  table  and  hold  it 
upright  by  any  convenient  means.  Back  of  it  and  resting  against  it, 
stand  a  card  having  a  horizontal  line  drawn  on  it  to  mark  the  level 
of  the  mercury  in  the  two  arms  of  the  tube.  To  one  ann  attach  the 
neck  of  a  funnel  by  means  of  a  bit  of  rubber  tubing.  The  funnel  may 
be  held  by  the  ring  of  a  retort  stand.  Pour  water  slowly  into  the 
funnel  until  nearly  full,  and  mark  the  level  of  the  water  by  a  sus- 
pended weight  or  other  means.  In  one  arm  the  mercury  will  be 
depressed  below  the  line  marked  on  the  card  ;  in  the  other  arm  it  will 
be  raised  above  it  an  equal  distance.  Mark  these  two  mercury  levels 
by  dotted  horizontal  lines  on  the  card.  Remove  the  funnel  and  re- 
place it  by  a  funnel  or  "  thistle  "  tube,  making  the  connection  by  means 
of  a  perforated  cork.  Pour  water  into  the  funnel  tube  until  it  stands 
at  the  level  indicated  by  the  suspended  weight,  being  careful  that  no 
air  is  confined  by  the  teater  in  the  tubes.  Although  much  less  water 
is  in  the  funnel  tube  than  was  in  the  funnel,  it  forces  the  mercury 
into  the  position  indicated  by  the  dotted  lines  on  the  card  The  down- 
ward pressure  of  the  water  in  each  case  is  measured  by  a  mercury 
column  with  a  height  equal  to  the  vertical  distance  between  the  two 
dotted  lines.     See  First  Prin.  Nat.  Phil.,  Exps.  45,  47. 

Exercises,  Page  127 » 

1.  (See  §  231.)  The  imaginary  column  has  a  base  of 
30  x  20  and  an  altitude  of  10  ft.  Cubic  contents  =  6000 
cu.  ft.  The  weight  of  6000  cu.  ft.  of  water  is  (§  226,  note) 
62.42  lb.  x  6000  =  374520  lb.—  Ans. 

Suggestion.— Allow  the  pupil  to  use  62|  lb.  as  the  weight  of  a 
cu.  ft.  of  water,  if  he  prefers  to  do  so.  That  value  is  more  easily  re- 
membered, and  nearly  enough  accurate  for  non -professional  purposes. 

2.  Bulk  of  imaginary  column  =  (6  x  10  x  3  =)  180 
cu.  m.  =  180  Kl.  =  180000  liters.  (§  29.)  Each  liter 
of  water  weighs  1  Kg.  (§  36.)  Hence  the  pressure  is 
180000  Kg. 

3.  5  x  12  x  6  =  360,  the  number  of  cu.  ft. 
62.42  lb.  x  360  =  22471.2  lb.— Ans. 

4.  2  x  4  x  2  =  16,  the  number  of  cu.  m. 

16  cu.  m.  —  16,000  I,  which  weigh  16,000  Kg.— Ans, 


[Element*  of  Xuturul  Philosophy,  p.  127.]  99 

5.  (See  §  226.)     2  cu.  yd.  =  54  cu.  ft. 
62.43  lb.x54  =  3370.08  lb.—  Am. 

6.  2cu.m.  =  2000  I 

2000  /.  of  water  weigh  2000  Kg.— Am. 

7.  (See  §  228.)    25  cu.  ft.  of  water  weigh  (62.42  lb.x 
25  =)  1560.5  lb.— Am. 

8.  30  x  30  x  800  =  720000,  the  number  of  cu.  cm.  This 
quantity  of  water  weighs  720000  g.  or  720  Kg.— Am. 

9.  3  x  3  x  7  =  63,  the  number  of  cu.  ft. 
62.42  lb.  x  63  =  3932.46  lb.— Am. 

10.  The  dimensions  of  the  vessel  are  12  x  12  x  12.  The 
acid  stands  8  in.  deep.  12  x  8  x  4  =  384,  the  number  of  cu. 
inches  in  the  imaginary  column.  This  is  f  of  a  cu.  ft.  If 
the  imaginary  column  were  of  water,  it  would  weigh  f  of 
62.42  lb.  =  13.871+  lb.  Such  a  column  of  acid  would 
weigh  1.8  times  13.871+  lb.  =  24.9678+  lb.—  Am. 

11.  237  x  35  =  8295,  the  number  of  cu.  cm.,  and  conse- 
quently the  number  of  grams. 

12.  237  x  35  =  8295,  the  number  of  cu.  in. 

62.42  lb.  x  fffrl  =  299.7  Ik— Am.     (See  §  24.) 

13.  The  water  must  stand  (V  =)  H  * k  deep.  The 
sides  subjected  to  lateral  pressure  hare  an  area  of  (10  x 
4£  =  )  45  sq.  ft.  45  x  2J=101J,  the  number  of  cu.  ft.  in  the 
imaginary  column  producing  lateral  pressure.  There  are 
27  cu.  ft.  (2  x  3  x  4~£)  in  the  column  producing  pressure 
on  the  bottom.     101.25  +  27  =  128.25. 

62.42  lb.  x  128.25  =  7999.365  lb.— Am. 

14.  If  the  lever  of  the  press  be  of  the  second  class,  as 
ibowu  in  Fig.  70,  the  piston  of  the  pump  will  <ro  down 
wiih  a  force  of  (75  lb.  x6  =)  450  lb.  The  area  of  the 
cylinder  being  200  times  greater  than  that  of  the  piston, 
the  weight  will  be  200  times  450  lb.,  or  45  tons.     If  the 


100  Elements  of  Natural  Philosophy,  pp.  137-130.]        # 

lever  be  of  the  first  class,  the  weight  will  be  (75  lb.  x  5  x 
200  s=)  75,000  lb.  =  37J  tons. 

15.  2  x  3  x  5  =  30,  the  number  of  cu.  ft. 
62.42  lb.  x  30  =  1872.6  lb.— Am. 

16.  (See  Appendix  A.) 

Area  =  nX*  =  3.1416  x  100  =  314.16. 
314.16  x  48  =  15,079.68,  the  number  of  cu.  in. 
15,079.68  cu.  in.  =  8.72  cu.  ft. 
62.42  lb.  x  8.72  =  544.3  +  lb.—  Arts. 

§234(6).  See  Descbanel's  "Natural  Philosophy," 
§§  90-92. 

§  235.  A  very  learned  article  on  "  Capillary  Action,"  by 
Prof.  J".  Clerk  Maxwell,  may  be  found  in  Vol.  V,  of  the 
*  Encyclopaedia  Britannica,"  9th  edition.  See  Deschanel's 
"  Natural  Philosophy,"  §§  97,  98.    See  Note  on  p.  102 

§  236.  The  interdiif  usion  of  fluids  separated  by  a  porous 
partition  is  called  osmose. 

Tie  a  piece  of  bladder  or  parchment  paper  over  the  mouth  of  a 
glass  funnel.  Nearly  fill  the  vessel  thus  made  with  a  concentrated 
solution  of  copper  sulphate  (blue  vitriol).  Suspend  the  funnel  and 
its  contents  in  a  vessel  of  clear  water.  In  about  an  hour,  it  may  be 
noticed  that  the  vitriol  solution  has  increased  in  volume  and  stands 
higher  than  it  originally  did  in  the  neck  of  the  inverted  funnel.  The 
water  in  the  onter  vessel  will  be  tinged  blue.  Evidently,  some  of 
the  vitriol  solution  passed  outward  through  the  septum  while  a 
greater  quantity  of  water  passed  inward.  A  bladder,  into  the  mouth 
of  which  a  glass  tube  has  been  snugly  tied,  may  be  used  instead  of 
the  funnel  and  membrane.    See  Etem.  Chemistry,  Exp.  21. 

The  flow  of  the  fluid  toward  that  which  increases  in 
volume  is  called  endosmose  ;  the  opposite  motion  is  called 
exosmose. 

Graham  divided  substances  into  two  classes,  crystalloids 
and  colloids  (crystal-like  and  gum -like).  The  former  easily 
diffuse  through  porous  septa  ;  the  latter  do  not.  The 
application  of  the  principle  of  osmose  to  the  separation  of 


[Elements  of  S>'      *    I'hilomphy,  pp.   MO-lty.]  101 

rnstalloids  and  colloids  is  called  dia  For  instance, 

if  the  liquid  contents  of  the  stomach  |jf  I  dead   a;>i.c;d 
poisoned  with  arsenic  or  strychniiu  .be.  placed  in  a  '//< 

ua\ing  a  parehincui.  bottom  |  avid  -  i][opteA*.pft; 
water,  the  poisonous  crystalloids  will  pass  through  into 
the  water  and  may  thence  be  easily  obtained.     The  albu- 
minous contents  of  the  stomach  (i.  e.,  the  colloids)  will  be 
held  back  by  the  septum. 

§  239.  See  Pickering's  "  Physical  Manipulation,"  p.  89. 

§  240.  See  First  Prin.  Nat.  Phil,  Exp.  52  and  §  163. 

I .n  irises,  Page  134. 

1.  It  will  lose  the  weight  of  I  cu.  dm.  of  water.  (§  238.) 
This  is  the  weight  of  a  liter  of  water,  1,000  g.  or  1  Kg. 

2.  It  would  lose  the  weight  of  1  cu.  dm.,  or  1  liter  of 
the  lie  pi  id  (mercury),  which  would  weigh  13.6  times  1  Kg., 
or  13.6  Kg.  =  13,600  g. 

3.  The  iron  is  supposed  to  be  immersed  in  the  mercury. 
The  mercury  pushes  it  up  with  a  force  of  13,600  g.  Grav- 
ity ]  ml  Is  it  down  with  a  force  of  7,780  g.  It  must  be  held 
down  by  an  additional  force  of  5,820  g.  It  can  carry  a 
load  of  5,820  g.  If  the  iron  be  allowed  to  float  on  the  mer- 
cury, it  will  displace  only  7,780  g.  of  mercury,  thus  losing 
its  own  weight.     (§  240.) 

4.  The  weight  of  a  cu.  ft.  of  water,  or  62.42  lb.   (§  238.) 

5.  It  will  displace  100  cu.  cm.  of  water.  (§  237.)  It  will 
therefore  lose  100  g.  in  weight.  (§§  36,  238.)  The  re- 
maining weight  will  be  1,035  g. 

6.  It  loses  10  g.  in  weight  when  placed  in  water.  It 
therefore  displaces  10  g.  or  10  cu.  cm.  of  water;  its  own 
bulk  is  10  cu.  cm. 

7.  It  loses  10  oz.  in  weight  when  placed  in  water.  It 
therefore  displaces  10  oz.  of  water.  10  oz.  of  water  is 
(TJflT  =)  -^  of  a  cubic  foot  of  water  or  17.28  cu.  inches, 
(See  §226,  note.) 


102  [Elements  of  Natural  Philosophy,  pp.  134-141.] 

§  250.  To  prevent  the  instrument  from  sinking  so  as  to 
wet;  the  pan/tt,  ilirtl  te  keep  the  hydrometer  from  touching 
the  side  of  the  jar,  it  is  well  to  place  a  wire  fork  on  top  of 
x\vs  ia;y^  that  its  two  prongs  shall  embrace  the  rod  sup- 
porting a. 

For  a  cheap  substitute  for  this  instrument,  see  Frick's 
"  Physical  Technics,"  Fig.  145. 

§  252.  Make  a  pine  rod  about  a  foot  long  and  exactly 

half  an  inch  square.     Graduate  it  to  quarter  inches.     In 

the  end  of  the  rod  (at  which  your  scale  begins),  bore  a  hole 

just  large  enough  to  allow  lead  bullets  to  enter  snugly. 

Drive  enough  bullets  into  this  hole  to  make  the  rod  sink 

in  water  to  the  8  inch  mark  on  the  scale.     Dry  the  rod 

and  dip  it  for  a  few  moments  in  melted  (very  hot)  paraffine 

wax  to  prevent  it  from  again  absorbing  water.    Adjust  it 

by  loading  or  cutting  away  at  the  upper  end   until,  in 

vvaterv  it  will  sink  exactly  to  the  8  inch  mark.     It  will 

then  displace  2  cubic  inches  of  water,  or  the  rod  weighs  as 

much  as  2  cubic  inches  of  tvater  (§  240).    Next,  place  it 

in  alcohol.     Suppose  that  it  sinks  to  the  10  inch  mark. 

Then  it  displaces  (*£■  =)  2.5  cubic  inches  of  alcohol,  or 

the  rod  weighs  as  much  as  2.5  cubic  inches  of  alcohol. 

Therefore,  2.5  cu.  in.  of  alcohol  weighs  the  same  as  2  cu. 

in.  of  water,  for  they  both  weigh  the  same  as  the  rod. 

2 
Then  the  alcohol,  bulk  for  bulk,  is  —  times  as  heavy  as 

water.      This    means    that    the    sp.    gr.    of    alcohol    is 
/  2 


=)», 


p-  •* 

Note. — A  source  of  frequent  error  in  using  hydrometers  is  stated 
in  Daniell's  "  Principles  of  Physics,"  p.  257.  The  subjects  of  surface 
tension  and  surface  tenacity  or  viscosity  and  the  relation  of  the  former 
to  capillary  attraction,  as  well  as  of  osmose  and  dialysis  are  treated 
on  pp.  252-256  of  that  work.  A  valuable  article  on  capillary  attrac- 
tion may  be  found  in  "  Nature,"  Vol.  34,  p.  270. 


[Element*  of  Natural  Philosophy.]  103 


isrs,   Ptujv   142. 

Note. — If  you  have  kept  up  the  written  reviews  recommended 
on  p.  39  of  this  Hand-book,  you  may  have  found  that  some  of  the 
pupils  have  frequently  forgotten  or  failed  to  do  the  work.  Allow  no 
such  case  to  escape  your  careful  notice.  Require  the  performance 
of  the  work,  unless  for  -eery  go*>d  reason.  If  the  pupil  cannot  solve 
any  given  problem,  give  him  the  needed  help  and  then  require  tbt 
written  $oiutim.  When  the  indolent  pupil  finds  that  he  cannot 
escape  this  work,  he  will  cease  to  try  to  escape.  If  a  pupil  needs 
help,  he  should  get  it  from  the  teacher  in  time  to  have  his  written 
solution  ready  when  it  is  due.  Analogy  :  When  a  bank  note  is  not 
paid  before  the  close  of  banking  hours  on  the  day  of  maturity,  the 
note  goes  to  protest.  The  matter  cannot  be  settled  by  handing  in  the 
money  "the  next  morning,"  without  an  additional  payment  for  the 
cost  of  the  protest,  as  a  penalty.  Even  then,  the  business  credit  of 
the  delinquent  has  suffered. 

For  examples  t  to  10,  see  table  on  page  43. 

Suggestions  concerning  the  above  exercises : 

(1.)  First  fill  blank  in  column  marked  (c);  1500—1000  =  500. 
Then  fill  blank  in  (</.);  1500  lb.  +  500  lb.  =■  3.  Then  fill  blank  in 
K);  the  body  loses  500  lb.  in  water,  which  shows  that  it  displays 
500  lb.  of  water  (g  238),  or  8  cu.  ft.  of  water.  Hence  (§  237),  8  cu.  ft 
is  the  volume  of  the  body.  Now  fill  the  blank  in  {g.\  In  a  fluid 
\\  times  as  heavy  as  water,  it  will  lose  \\  times  as  much  weight  as 
it  does  in  water,  or  750  lb.  As  it  weighs  1500  lb.  in  air  and  loses 
750  lb.  in  this  fluid,  it  weighs  (1500—750  — )  750  lb.  in  the  fluid. 

(2.)  First  fill  blanks  in  (b.),  (d.),  and  (e.),  in  their  order.  In  the 
fluid  in  question,  the  body  loses  3000  oz.,  or  twice  as  much  as  it 
does  in  water-  The  volumes  of  the  two  fluids  displaced  being  equal 
(§  247),  the  specific  gravity  of  the  second  fluid  is  2. 

(3.)  Fill  (a.)  (see  §  244).    2  =  ^—5^.    .-.  IT  =  3750.     Then 

fill  (e.)  and  («.).     If  it  loses  1875  g.  in  water,  it  will  lose  1.8  times  as 
much  in  the  required  fluid.    3750  g.  —  3o75#.  s  375  g. 

(4 )  Let  x  —  loss  of  weight  in  water.  Then  will  \x  =  loss  of 
weight  in  the  other  fluid.  The  weight  in  air  =  9375  +  x  =  4687|  +  fx. 
.".  x  =  9675  g.  This  value  fills  blank  in  (c).  Now  fill  blank  in  (a.) 
(&),  and  (e.),  in  order. 


104 


[Elements  of  Natural  Philosophy,  p.  142.] 


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8  § 


(5.)  That  volume  of  water  would  weigli  300  #.  This  body  will 
weigh  7.5  times  300  g.  =  2250  g.,  the  answer  for  (a.).  It  will  dis- 
place 300  cu.  cm.  of  water,  and,  consequently,  lose  300  g.  when 
weighed  in  water.  This  is  the  answer  for  (c).  Find  the  answer  for 
(&.).  Multiply  (c.)  by  2.5,  and  subtract  the  product  from  (a.)  for  the 
value  for  (g.). 


(6.)  Solve  in  the  same  manner  as  the  4th. 


[Elements  of  Natural  Philosophy,  pp.  14S,  14S.]  105 

(7.)  62  \  lb.  x8  =  500  lb.,  the  value  for  («.)•  5001b.  x  13.6=6800  lb, 
the  loss  in  the  heavy  fluid  (mercury).  6800  lb.  +2700  lb.  =  9500  lb., 
the  value  for  (a.). 

(8.)  From  (e.)  we  see  that  the  value  for(c.)  is  5000  #.  Multiplying 
this  by  6.80,  we  have  34300  g.  for  (a  ).  The  loss  in  water  x  13.6  = 
68000  g.,  the  loss  in  mercury.  Hence,  the  body  will  support  a  load 
of  33700  g.  on  mercury. 

(9.)  Sp.  gr.  being  unity,  the  body  is  water  or  something  equally 
heavy. 

(10.)  Fill  the  blanks  in  this  order  :  (&),  (a.),  (6.),  (g.). 

11.  6.6  oz.  —  2.6  oz.  =  4  oz. 

6.6  oz.  -r-  4  oz.  =  1.65,  the  sp.  gr. 

12.  453  g.  —  429.6  g.  =  23.4  g. 

453  #.  -T-  23.4  g.  —  19.36,  nearly.—  Ans. 

13.  52.35  g.  +  hg.  =  10.47,  the  sp.  gr.  of  silver.  (§  253.) 

14.  (a.)   695  g.  -±%Zg.  =  8.37+,  the  sp.  gr.  of  brass. 
(b.)   83.^.x. 792  =  65.736  g. 

695  g.  —  65.736  g.   =  629.264  g.—Ans. 

15.  708  gr.  -r-  1000  gr.  =  .708,  the  sp.  gr.  of  the  benzo- 
line. 

16.  2.4554  oz.  -  2.0778  oz.  =  .3776  oz. 
2.4554  oz.  -T-  .3776  oz.  =  6.5  +  .— Ans. 

17.  4.6764  oz.  -r-  .2447  oz.  =  19.11,  the  sp.  gr.  of  the 
gold. 

18.  (§  247.)  970  gr.  —  895  gr.  =  75  gr. 
970  gr.  —  910  gr.  =  60  gr. 

60  gr.  -=-  75  gr.  =  .8.— Ans. 

19.  (§  247.)  23  gr.  -f-  25  gr.  =  .92,  sp.  gr.  of  the  oil. 
19  gr.  -r-  25  gr.  =  .76,  sp.  gr.  of  the  alcohol 

20.  1536  g.  —  1283  g.  =  253  g. 
1536  g.  +  253  g.   =  6.07.—  Ans. 


106  [Elements  of  Natural  Philosophy,  p.  1Ji$.\ 

21.  Subtract  the  weight  of  bottle  from  the  other  two 
weights.    4.2544  g.  -~  4.1417  g.  =  1.027  +  .— ^4  w*. 

22.  (1.)  Weight  of  wood  and  sinker  in  air,  14=  g. 
(2.)        "        "          "            "           water,  8.5  g. 
(3.)        "        "  water  displaced  by  both,  5.5  g. 
(4.)        "        "           "               "      sinker 

(10^.^-16.5=) .954:  g. 

(5.)  Weight  of  water  displaced  by  wood,       4.546  g, 
(6.)  Sp.  gr.  of  the  wood  (4  g.  -*-  4.546  g.  =)    .897 

23.  Sp.  gr.  of  metal  is  1.73 ;  of  the  unknown  liquid,  0.67. 

24.  2160  gr.  —  1511.5  gr.  =  648.5  gr. 
2160  gr.  <*!  648.5  gr.  =  3.33  +  .— Ans. 

25.  (1.)  Weight  of  ice  and  lead  in  air,  -    -    24  lb. 
(2.)         "       "  "  "     water,  -    13.712  lb. 

(3.)        "       u  water  displaced  by  ice 

and  lead, 10.288  1b. 

(4.)  Weight  of  water  displaced  by  lead,      1.4      lb. 

(5.)         "       "  "  "      ice,      ~~&888  1b. 

(6.)  Sp.  gr.  of  ice  (8  lb.  4-  8.888  lb.  =)       .9+. 

26.  (a.)  600  g.  —  545  g.  =  55  g. 

600  g.  -£-  55  g.  =  10.9  +  .—  Ans. 
(b.)   600  g.  —  557  g.  =  43  g. 

43  g.  -r-  55  g.  —  .78  +  .  —Ans. 
(c.)   600  cu.  cm.  -T-  10.9  =  55+  cu.  cm. — Ans. 

27.  The  simple  question  is,  "  How  much  does  that  stone 
weigh  in  water  ?  " 

(§  244.)    2.5  =  3o^r,-  .<  W  =  180  Vo.-Am. 

28.  An  equal  bulk  of  water  weighs  1000  g. 

870  #.-r-1000#.  =  .87,  the  sp.  gr.  of  the  turpentine. 

29.  The  volume  of  the  fragments  was  1000  cu.  cm.  — 
675  cu.  cm.  =  325  cu.  cm.      The    fragments    weighed 


[Bkmenit  of  Natural  Philosophy,  pp.  W,  1U-]  1°? 

1487.5  g.  —  C75  g.  =  812.5  g.     An  equal  bulk  of  watei 
would  weigh  325  g. 

812.5  g.  -T-  325  g.  =  2.5,  the  sp.  gr.  of  the  mineral 

30.  (See  §  29.)  The  800  cu.  cm.  of  water  weigh  800  g. 
The  200  cu.  cm.  of  sand  weigh  1350  g.  —  800  g.  =  550  g. 
An  equal  bulk  of  water  weighs  200  g.  550  g.  -r-  200  g.  ss 
2.75,  the  sp.  gr.  of  the  sand. 

31.  Sp.  gr.  ss jstt —  =  8> tne  8P-  £?•  °?  tne  DraS8- 

(§  250.) 

o^    ci  2000  -f-  3400       l  _     , ,  -  ,, 

32.  Sp.  gr.  =  2000  +  1000  =  L8'  the  **'  &'  °f  the 
acid.    (§251.) 

33.  The  given  body  weighs  10  g.  It  displaces  2.5  g.  of 
Water  (an  equal  bulk  of  water  weighs  2.5  g.). 

10  g.  ■+■  2.5  g.  =  4,  the  sp.  gr. 

34.  1  cu.  Km.  =  1000  cu.  Hm.  =  1000000  cu.  Dm.  — 
1000000000  cw.  m.  =  1000000000000  cu.  dm.  or  liters. 
Then,  1  cu.  Km.  of  water  would  weigh  1000000000000  Kg., 
and  1  cu.  Km.  of  earth  of  the  assumed  density  would 
weigh  5660400000000  Kg.  (56604  x  108.)  Multiply  the 
weight  of  1  cu.  Km.  by  the  number  of  cu.  Km.: 

(56604  x  108)  Kg.  x  1082842  x  10»= (61293188568  x  101')  Kg. 
Suggestion. — To  multiply  by  1017,  add  17  ciphers. 

35.  427.40  mg.  -7-  2545  mg.  =  16.793  +  .  This  means 
that  mercury  is  16.793+  times  as  heavy  as  alcohol.  But 
alcohol  is  .8095  times  as  heavy  as  water.  Hence  mercury 
is  (16.793+  x  .8095  =)  13.59+  times  as  heavy  as  water. 
Sp.  gr.  of  the  mercury  =  13.59  +  . 

Dividing  5829  mg.  by  2545  mg.f  we  find  that  the  acid  is 
2.29+  times  as  heavy  as  alcohol.  Multiplying  this  2.29  + 
by  .8095,  we  find  that  the  acid  is  1.853  +  times  as  heavj 
as  water.     Sp.  gr.  of  the  sulphuric  acid  =  1.853  + 


108  [Elements  of  Natural  Philosophy,  p.  144-] 

36.  (1.)  Weight  of  both  in  air, 41.2  # 

(2.)         "        «  "     water, 2C.2  g. 

(3.)  "      lost  by  both  in  water,    -    -    -  15  g. 

(4.)  «            "      iron    "       "        -    -    -  5  g. 

(5.)  *            *      cork   "       *        ...  10^. 

(6.)  Sp.gr.  of  cork  (2.3 -*- 10  =)      -    -    -        .23. 

37.  (*)  (See  §244.)    Sp.gr.  =  jf^gr 

-    ^  =  60&'       .'.r- 547.13+. 

The  lead  weighs  547.13+  gr.  in  water. 
(b.)    (1.)  Weight  of  both  in  air,   -     -     -     900  gr. 
(2.)        "       "         "     water,    -    -    472.5  gr. 
(3.)        "      lost  by  both  in  water,      427.5  gr. 
(4.)        «  "      lead        "  52.87  gr 

(5.)         *  "      wood      "  374.63  gr 

(6.)  Sp.  gr.  of  wood  (300  gr.-^374.G3  gr.  =  )  .8  + 


38.         111.7050  g. 
14.1256  #. 


111.1370  #« 
14.1256  #. 


97.5794  #.    ~     97.0114  ^  =  1.0058  +  .— -4*w. 


618  gr. 
31  gr. 


618  gr. 
93  gr. 


649  gr.    -7-  711  gr.  =;  .9  +  .—  Ans. 

40.  (a)   330  g.  —  315  #.  =  15  g. 

330  g.  -^  15  g.  =  22.— Ans. 
(i.)   330  g.  —  303  f.  =  27  0, 

27  jgr.  -+  15.gr.  =  1.8.— 4*w.     (§  247.) 
(c.)    It  displaces  15  g.  or  15  cw.  cw.  of  water. 

Its  volume  is  15  cu.  cm. 

41.  Its  volume  must  be  at  least  that  of  1  Kg.  of  water. 
(§  240. )  The  volume  of  1  Kg.  of  water  is  1  liter,  1  cu.  dm., 
or  1000  cu.  cm. 


[Elements  of  Natural  Philosophy,  pp.  144.  145.]  109 

42.  The  lead  will  displace  10  cu.  cm.  of  water,  and  con- 
sequently lose  10  g.  in  weight.  If  both  lose  159  g.  in  water, 
and  the  lead  loses  10  g.,  the  cork  will  lose  149  g. 

30  g.  -r-  149  g.  =  .201,  the  sp.  gr.  of  the  cork. 

37 

43.  (See  §  244.)     2.8  =  ^  _W>' 

/.   W  =  23.785+  g.—Ans. 
Or,  we  may  say  that  the  body  being  2.8  times  as  heavy 
as  water,  an  equal  bulk  of  water  would  weigh  ~  grams  = 
13.2142+  g.     This  is  what  the  body  would  lose  in  water. 
(§  238.)     37 g.  —  13.2142+  g.  =  23.785+  g.—Ans. 

44.  The  coal  would  weigh  2.4  times  as  much  as  a  cubic 
foot  of  water  or  (62.5  lb.  x  2.4  =)  150  lb.  It  would  dis- 
place 1  cu.  ft.  of  the  solution,  which  would  weigh  (62.5  lb. 

x  1.2  =)  75  lb.     It  will  lose  75  lb.  weight  when  in  the 
saline  solution.     150  lb.  —  75  lb.  =  75  lb — Ans. 

Or,  we  may  say  that  the  coal  will  weigh  as  much  as 
2.4  cu.  ft.  of  water,  and  that  the  solution  displaced  by  it 
will  weigh  as  much  as  1.2  cu.  ft.  of  water.  The  weight 
less  the  loss  by  buoyancy  will  be  the  weight  of  (2.4  cu.  ft. 
—  1.2  cu.  ft.  =)  1.2  cu.  ft.  of  water,  or  75  lb.— Ans. 

45.  The  loss  of  weight  in  water  will  be  -^  g.  The  loss 
of  weight  in  mercury  will  be  *$£■  g.  x  13.6  =  185.45+  g. 

300  g.  —  185.45+  g.  =  114.54+  g.—Ans. 

46.  With  a  force  equal  to  the  weight  of  the  iron.  (§  240.) 

500  g.  x  7.8  =  3900  g. 

47.  (See  §  249.) 

v,  the  volume  of  water  displaced,  weighs  600  gr. 

&v,      "  "     acid  "  «      600  gr. 

In  order  to  compare  the  sp.  gravities  of  these  two  liquids, 

we  must  find  the  weights  of  equal  volumes.    Thus,  we  may 

find  the  weight  of  a  volume  of  the  acid  equal  to  v,  the 

given  volume  of  water,  or  we  may  find  the  weight  of  a 


110  [Elements  of  Natural  Philosophy,  pp.  145-153. ,] 

volume  of  the  water  equal  to  -ftv,  the  given  volume  of  the 
acid.     Suppose  we  try  the  latter  method. 

ft-v  of  acid  weighs  600    gr. 

-ft-v  of  water  weighs  (ft  of  600  gr.  =)     337|  gr. 
(See  §  243.)     600  gr.  -j-  337£  gr.  —  1.8,  nearly.— Ans. 

As  a  matter  of  fact,  the  weight  of  the  areometer  is  not 
an  essential  part  of  the  problem,  for,  inasmuch  as  it  takes 
only  ft^  as  much  of  acid  as  it  does  of  water  to  equal  the 
(unknown)  weight  of  the  areometer,  the  acid  must  be  -^ 
as  heavy  as  the  water.     *$■  =s  1.8,  nearly. 

Note. — In  keeping  up  the  written  reviews,  you  may  have  noticed 
that  the  pupils  * '  work  together,"  or  help  one  another.  If  you  have 
not  noticed  it,  look  for  it.  If  you  find  that  the  practice  prevails  in 
your  class,  try  to  have  each  pupil  do  his  work  independently.  Show 
the  pupil  kindly  that  in  this  way  only  can  he  get  the  greatest  possi- 
ble good  from  the  study  ;  that  it  is  not  so  much  what  another  does 
for  him  as  what  he  does  for  himself  that  gives  him  mental  strength. 
Show  him  that  what  you  recommend  is  the  honest  course  for  him  to 
follow.  He  should  not  deceive  you,  even  unintentionally,  into  the 
belief  that  he  is  strong  enough  to  do  the  work  of  the  class  when  he 
is  not.  Show  bim  that  here,  as  elsewhere,  honesty  is  the  best  policy, 
because,  judging  from  his  satisfactory  papers,  you  think  that  he  does 
not  need  your  special  attention,  which  is,  consequently,  given  else- 
where. Show  him  that  the  course  from  which  you  would  lead 
him  is  unmanly ;  that  asking  a  classmate  for  help  or  accepting  his 
help,  is  a  confession  of  mental  inferiority,  while  the  proffering  of 
unasked  assistance  is  (essentially)  an  insulting  assumption  of  supe- 
riority. 


[Moments  of  A  WUmpkg,  pp.  153,  /•*;.]  111 

■>4  (e).  See  Ex.  6,  p.  154  of  text-book.  The  teacher 
will  find  a  pretty  Experiment  at  the  bottom  of  page  282 
Of  Darnell's  u  Principles  of  Physics." 

§  267  (a).  The  u  hydraulic  nun  "  will  be  easily  under- 
stood from  the  accompanying  figure.  The  water-supply  is 
represented  by  the  reservoir,  A.  The  valves  at  S  and  8' 
being  down,  S  is  open  and  S'  closed,  as  shown  in  the  cut. 
The  water  from  A,  flowing  through  //and  escaping  at  S, 
soon  acquires  sufficient  velocity  (see  §  156)  to  overcome 
the  gravity  of  S  and  close  the  valve.  The  weight  of  S  is 
adjusted  for  this  purpose.  The  water,  thus  suddenly 
checked  in  its  flow,  opens  the  valve,  S',  and  enters  the  air- 
chamber  at  r,  covering  the  lower  end  of  the  delivery-tube, 
T,  and  compressing  the  air  in  the  air-chamber  (§  297). 
The  water  in  H,  having  lost  its  motion,  is  uo  longer  able 
to  support  the  properly  weighted  valves;  S  and  S'  are 
both  drawn  down  by  the  force  of  gravity.  S  being  now 
open  again,  the  water  begins  to  flow  along  H  and  again  to 
escape  at  C,  the  water  in  the  air-chamber  being  prevented 
Dy  &  from  returning.  As  the  velocity  of  the  water  flow 
ing  through  H  increases,  the  valves  are  again  lifted  and 
the  process  repeated.  The  air  in  the  air-chamber  being 
greatly  compressed,  forces  the  water  out,  through  the 
delivery-pipe,  to  a  height  greater  than  that  of  A, 


112       [Elements  of  Natural  Philosophy,  pp.  154, 155^ 


[Element*  of  Natural  Philosophy.]  113 

Ejrrrrists,   Vtujv  153. 

1.  v  =  8.02^169=8.02  x  13  =  104.26,  the  number  of  ft. 

2.  v  =  8.02 Vl2  =  8.02x3.46  =  27.75. 

27.75  ft.  =  333  in. 

333  x  ^  X  60  x  60  =  119,880,  the  number  of  cu.  in. 

119,880  -i-  231  ss  519—,  the  number  of  gallons. 

3.  v  =  8.02V25  =  40.1.     40.1  ft  =  481.2  in. 

481.2  cu.  in.  x  2  x  60  x  60  =  3,464,640  cu.  in. 

=  14,998-f  gal.  or  2,005  cu.  ft 

4.  96.24  =  8.02v^;  12  =  </h ;  144  =  h. 

Ans.,  144  ft 

5.  The  water  falls  during  one  second.     (§  126.)     The 
range  of  80.2  ft.,  therefore,  represents  the  velocity.  (§  135.) 

80.2  =  S.02Vh  ;  10  =  Vh  \  100  =  h. 

Ans.y  100  ft. 

6.  In  the  last  equation  of  §  254,  c,  take  the  value  of  2g 
in  meters  (§  127)  instead  of  feet: 

v  =  V2gh  =  V19.6A  =  4.427VA. 

7.  Ans.,  22.135  m. 

8.  v  =  26.562  m.  =  2,656.2  cm. 

2,656.2  x  10  x  20  =  531,240,  the  number  of  cu.  cm. 
531,240  cu.  cm.  =  531.24  liters.—  Ans. 

9.  v  =  44.27  m.  =  4,427  cm. 

4,427  x  1  =  4,427,  the  number  of  cu.  cm.  escaping  per 
second. 

442,700  cu.  cm.  -f-  4,427  cu.  cm.  =  100,  the  number 
of  seconds. — Ans. 


114  [Memento  of  Natural  Philosophy,  pp.  164,  155^ 

10.    v  =  4.427\/5  =  4.427  x  2.236  =  9.898772  m. 

=  989.877  cm. 
This  is  the  velocity  at  the  beginning,  when  the  head  is 
5  m.  The  head  (and  with  it,  the  velocity)  is  continually 
diminishing  to  zero.  Hence,  the  average  velocity  is  only 
half  as  great,  or  494.9386  cm.  The  average  flow  will  be 
494.9  cu.  cm.  per  second.  The  capacity  of  the  tank  is 
60  cu.  m.  or  60000000  cu.  cm. 

60000000-T-494.9  =  121236  +  ,  the  number  of  seconds. 
Ans.  1  da.  9  h.  40  min.  36  sec. 

Review  Questions,  Page  154. 

1.  (a.)    See  §  12,  and  note  at  foot  of  page  82. 

2.  (b.)    15  x  50  =  750.— Ans, 

64.32 

(§  157.) 
4.  (a.)  10  :  W  : :  D>  :  d* 


(c.)    -^  =  583.02,  the  number  of  foot-pounds. 


[731 


w  :  1470  ::  4000*  :  14000*; 
■w  =  120  1b.     (§106.) 

5.  (a.)  112.56  ft.     (b.)  257.28  ft.     (c.)  128.64  ft. 
(a.)  34.3  m.        (b.)  78.4  m.        (c.)  39.2  m. 

(§§127,128.) 

6.  «^*l»^2L*  _  583000  lb#  Deducting  J  of  this 
for  the  loss  by  friction,  we  have  left  388800  lb. — Ans. 

(§  2H-) 

Note. — The  pulleys  may  be  arranged  so  as  to  give  seven  parts  to 
the  cord.  (§  197.)  In  such  a  case,  substitute  7  for  the  factor  6  in 
the  solution  above,  or,  to  the  answer  above,  add  £  of  itself. 

7.  I  :  L  ::  N*  :  n\     (§§146,147.) 

(a.)  39.1  :  L  ::  625  :  3600.    .:  L  =  225.21  inches. 
Or,  993.3  :  L  ::  625  :  3600.     .\  L  =  5721.408  mm. 

=.  5.7214+  m. 
(b.)  39.1  :  25  ::  iV2  :  3600.     /.  N=  75.03. 


[Elements  of  Natural  Philosophy,  pp.  154,  155.]  115 

8.  (c.)  The  engine  can  do  GG000  foot-pounds  of  work 
per  minute.  (§155.)  It  throws  to  the  top  of  the  steeple 
528  lb.  of  water  each  minute.    60000-^528  =  125.    Hence, 

teeple  is  125  feet  high.     (§§  152,  15:5.) 

9.  Figure  the  lever.  Represent  the  length  of  the  short 
arm  (WF)  hy  x.  Then  will  the  length  of  the  lever  and  of 
the  bag  arm  (PF)  be  18  +  z. 

40fe  =  4£(18+z).    /.  x  =  2± ;    18  +  z  =  20J. 

The  length  of  the  lever  is  20J  inches;  that  of  the  short 
arm  is  2^  inches. 

10.  150  lb.  x  V  =  1500  lb.— Ans. 

11.  (a.)    See  the  figure  on  p.  32  of  this  Key. 

(b. )  §  (90  x  5)  =  300.     Any  weight  less  than  300  lb. 
can  be  raised. 

12.  (a.)  Figure  the  lever  under  both  conditions.  In  the 
first  case  the  arms  will  be  24  and  36  inches.  24  x  12  = 
36  x  8.  In  the  second  case  the  arras  will  be  25  and  35 
inches.  25  x  14  =  35  x  10.  The  fulcrum  must  be  moved 
1  inch.  See  the  solution  of  the  32d  problem  on  the  90th 
page  of  the  text-book. 

13.  The  diameter  of  the  circle  traversed  by  the  power  is 
14  ft.,  just  12  times  the  diameter  of  the  capstan  barrel 
There  are  four  men,  the  energy  of  one  being  used  to 
overcome  friction.  The  other  three  exert  a  power  o! 
(42  lb.  x  3  =)  126  lb.  The  effect  =  126  lb.  x  12  = 
1512  lb.     Or  we  may  proceed  as  follows  : 

P  :W::  d  :  D.     (§182.) 

168  :  W  ::  14  in.  :  14  ft. 

.-.     W  =  2016  lb. 
Deducting  }  of  this  for  friction,        504  lb. 

The  effect  produced  is  1512  lb. 


CHAPTER  V. 


§  271.  The  impenetrability 
compressibility,  and  elasticity  oi 
air  may  be  shown  by  inverting  a 
tumbler  over  a  cork  floating  on 
water,  and  then  lowering  and 
raising  the  glass.  The  experi- 
ment also  illustrates  the  principle 
of  the  diving-hell. 


§  272.  The  figure  below  illustrates  a  convenient  form 
of  apparatus  for  this  purpose.  The  balance  is  also  admira* 
bly  adapted  to  experiments  in  specific  gravity. 


§  273.  See  First  Prin.  Nat.  Phil,  Exps.  53-60. 


{Element*  of  Natural  Philosophy,  pp.  156-160.]  1 1  ? 

§  274.  See  Frick's  "  Physical  Technics,"  p.  108  (§  96). 

§  275.  Fill  a  hydrometer  jar  (Fig.  272)  with  watt  r  and 
invert  it  over  a  water  bath.  Atmospheric  pressure  above 
the  contained  water  column  Is  sustained  by  the  rigid  glass 
bottom  of  the  inverted  jar  and  the  column  is  supported 
by  the  pressure  of  the  atmosphere  on  the  exposed  BUrface 
of  the  water  in  the  bath.  Tie  a  piece  of  sheet  robber 
over  one  end  of  a  lamp  chimney  or  other  large  tube.  Fill 
this  vessel  with  water  and  invert  it  as  before.  The  down- 
ward pressure  of  the  atmosphere  above  the  liquid  column 
forces  the  rubber  inward  until  the  atmospheric  pressure 
Irom  above  plus  the  weight  of  the  supported  liquid 
column  equals  the  atmospheric  pressure  transmitted  from 
below  plus  the  tension  of  the  rubber  diaphragm. 

§ 278.  See  Deschanel's  "Natural  Philosophy,"  §§  105-110. 


118  [Elements  of  Natural  Philosophy. ] 

Exercises,  Page  162. 

1.  15  lb.  x  144  x  14£  =  31320  lb.— Jins. 

2.  ttB*  =  3.1416  x  16  =  50. 2G56,  the  number  of  square 
inches  of  surface.     15  lb.  x  50.2656  =  753.984  lb. — Ans. 

3.  The  room  contains  6000  cu.  ft.  or  10368000  cu.  in.  of 
air.  This  weighs  (.31  gr.  x  10368000  =)  3214080  gr.,  or 
459.154  lb.  Avoirdupois. 

4.  If  the  barometer- tube  had  a  sectional  area  of  1  sq.  cm., 
the  atmospheric  pressure  per  sq.  cm.  would  support  a  mer- 
cury column  containing  76  cu.  cm.  Such  a  column  of 
water  would  weigh  76  g. ;  such  a  column  of  mercury  would 
weigh  76  g.  x  13.6  ==  1033. 6  g. 

Each  side  of  the  cube  has  a  surface  of  100  sq.  cm.  The 
six  sides  have  a  surface  of  600  sq.  cm.  The  atmospheric 
pressure  being  1.0336  Kg.  per  sq.  cm.,  the  total  pressure  is 
1.0336  Kg.  x  600  =  620.16  Kg.— Ans. 

5.  It  loses  the  weight  of  1728  cu.  in.  of  air,  or  535.68  gr. 

(§  ^38.) 

6.  (a.)  The  trunk  has  a  horizontal  section  of  (2 \  x  3J=) 
8J  sq.  ft.,  or  1260  sq.  in.  15  lb.  x  1260  =  18900  lb.,  the 
downward  pressure  on  the  top  of  the  trunk.  If  the  trunk 
have  aflat  top,  its  area  will  be  the  same  as  that  of  the  hori- 
zontal section  (or  bottom)  of  the  trunk;  if  it  have  an 
arched  top,  the  total  pressure  on  the  upper  surface  will  be 
more  than  here  given,  the  excess  being  lateral  pressure, 
which  would  not  at  all  interfere  with  opening  the  trunk, 
even  if  the  air  were  exhausted  from  it.  The  downward 
pressure  would  not  be  affected  by  the  shape  of  the  top. 

(b.)  The  upivard  pressure  on  the  under  surface  of  the 
trunk  top  is  equal  to  the  downward  on  the  upper  surface. 

7.  The  solution  of  this  is  involved  in  the  solution  of  the 
fourth  above. 


[Elements  of  Natural  Philosophy,  p.  163.]  119 

8.  (a.)  The  capacity  of  the  room  is  320  cu.  m.  oi 
390000  /.  (§§  28,  29.)  1.293  g.  x  320000  =  413700  g.,  oi 
413.T0  Kg.     (§272.) 

(b.)  and  (c.)  The  surface  is  80  sq.  m.,  or  800000  sq.  cm. 
The  atmospheric  pressure  being  about  1  Kg.  to  the  sq.  cm., 
the  pressure  on  each  of  these  surfaces  is  about  800000  Kg. 

((/.)  The  surface  is  32  sq.  m.,  or  320000  sq.  cm.  The 
pressure  on  each  of  these  surfaces  is  320000  Kg. 

(e.)  The  surface  is  40  sq.  m.  or  400000  sq.  cm.  The 
pressure  on  each  of  these  surfaces  is  400000  Kg. 

(/.)  The  total  surface  of  the  room  is  3040000  sq.  cm. 
The  total  pressure  is  3040000  Kg. 

(g.)  The  outward  pressure  from  within  is  counter- 
balanced by  the  inward  pressure  from  without. 

9.  A  liter  of  hydrogen  weighs  .0896  g. ;  10  liters  weigh 
.896  g.  The  balloon  and  hydrogen  weigh  5.896  g.  The 
10  /.  of  displaced  air  weigh  12.93  g.     (§  272.)  ' 

12.93  g.  -  5.896  g.  =  7.034  g.—Ans. 


120  {Elements  of  Natural  Philosophy,  pp.  163-167.] 

§  282.  When  definite  quantities  of  different  gases  or 
vapors  are  mixed  in  a  closed  vessel,  the  pressure  of  each 
is  added  to  that  of  the  others ;  the  pressure  of  the  mix- 
ture is  the  sum  of  the  pressures  of  the  separate  gases. 
This  fact  shows  that  the  molecules  act  with  entire  inde- 
pendence and  that,  as  a  consequence,  no  internal  work 
needs  to  be  done  to  expand  a  gas.  This  conclusion  was 
experimentally  demonstrated  when  Joule  showed  that  a 
gas  is  not  cooled  when  it  expands  without  doing  external 
work. 

The  words  pressure,  tension  and  elastic  force  are  often 
used  interchangeably. 

Exercises,  Page  167  > 

1.  (a.)  Under  a  pressure  of  two  atmospheres. 
(b.)  Under  a  pressure  of  half  an  atmosphere. 

2.  Under  ordinary  circumstances  (§  272),  the  air  would 
weigh  3.1  grains.  To  get  10  times  as  much  air  into  this 
same  space  of  10  cu.  in.,  it  must  be  subjected  to  a  pressure 
of  10  atmospheres. 

3.  (a.)  500  cu.  cm.,  or  £  liter. 

(b.)  500  cu.  cm.     It  makes  no  difference  what  gas  is 
used. 

4.  Half  of  it. 

5.  (See  §  282.)     (a.)  20  lb.  to  the  sq.  inch. 

(b.)  15  lb.  4-  5  lb.  +  10  lb.  =  30  lb.,  the  tension  per 
sq.  inch. 

6.  (a.)  In  the  short  arm.  The  rising  of  the  barometer 
indicates  an  increase  of  atmospheric  pressure.  This  in- 
crease of  pressure  will  push  down  the  mercury  in  the  open 
air,  and,  consequently,  push  it  up  in  the  closed  arm. 


[Element*  of  I  />/<;/,  />p.  168-170.]  KM 

7.  If  the  tension  were  unchanged,  the  11  gr.  would 
occupy  ^  as  much  space  as  the  8  grains.  When  all  oi 
this  air  is  forced  into  the  rigid  vessel,  its  volume  is  only  -^r 
what  it  was  under  a  tension  of  KiJ  lb.  The  volume  being 
•j8!-  of  the  original  volume,  the  tension  will  be  *£■  of  the 
original  tension ;  -y-  of  li\\  lb.  =  22  lb.  11  oz. 


§  288.     The  accompanying  figure  illustrates  the  con 
struction  of  the  valves,  etc.,  in 
Ritchie's  patent  air-pump. 

The  lower  valve  is  conical,  held  in 
place  by  a  triangular  stem  fitting  the 
tube;  it  is  raised  by  the  valve-rod 
passing  up  through  a  stuffing-box  in 
the  piston.  The  attachment  is  made 
so  as  to  allow  a  motion  of  the  rod  side- 
fcrise,  so  that  any  slight  change  of 
form  of  the  packing  of  the  piston,  or 
stuffing  of  the  rod,  cannot  prevent  the 
valve  from  shutting  properly.  The 
cone  of  the  valve  is  ground  to  a  per- 
fect tit  to  its  seat;  but  the  valve  is 
also  furnished  with  a  disk  of  oiled  silk, 
which  projects  just  beyond  its  outer 
edge,  and  touches  the  flat  surface  of 
the  valve-seat;  the  valve  rod  extends 
up,  and  is  secured  in  a  hole  drilled  la 
the  upper  plate,  of  depth  to  allow  motion  vertically  to  open  the  valve. 

The  piston  is  of  thick  brass,  made  in  two  parts ;  the  upper  ptea 
has  a  conical  bearing,  ground  to  fit  a  cone  on  the  piston-rod,  which 
forms  the  piston-valve  ;  a  series  of  channels  gives  free  passage  for 
the  air ;  the  lower  plate  covers  the  end  of  the  rod,  allowing  motion 
to  open  the  valve.  A  third  valve,  made  of  oiled  silk,  is  placed  out- 
side the  cylinder.  In  the  thickness  of  the  upper  plate  of  the  cylin- 
der is  inserted  n  steel  lever,  one  end  of  which  covers  the  valve-rod ; 
the  other  end,  when  the  lower  valve  is  closed,  is  flush  with  the 
plate;  but  when  the  valve  is  raised,  it  projects  into  the  cylinder. 

In  action,  the  first  motion  upward  of  the  piston-rod  closes  the 


122  [Elements  of  Natural  Philosophy,  p.  170.] 

piston-valve  ;  the  first  motion  of  the  piston  opens  the  lower  valve  ; 
as  the  piston  ascends,  the  air  above  it  is  forced  out  through  the 
upper  valve  and  air  from  the  receiver  flows  uuobstructedly  into  the 
cylinder.  The  piston  strikes  the  end  of  the  lever  and,  at  the  instant 
of  arriving  at  the  top,  closes  the  lower  valve.  The  first  downward 
motion  of  the  piston-rod  opens  the  piston-valve  ;  the  air,  in  the  inter- 
stices above  the  piston,  which  is  then  of  normal  pressure,  distributes 
itself  throughout  the  cylinder,  but  none  can  pass  the  lower  valve 
back  into  the  receiver. 

In  selecting  an  air-pump,  remember  that  a  brass  plate 
for  holding  the  receiver  is  objectionable  as  it  is  so  easily 
scratched  or  indented.  Ground  glass  plates  are  often 
furnished,  but  in  school  laboratories  they  are  likely  to  be 
broken.  On  the  whole,  an  iron  plate  is,  probably,  prefer- 
able. The  oil  used  will  generally  protect  it  from  rust.  A 
little  lard,  sperm  or  sweet  oil  should  be  occasionally  poured 
into  the  cup  at  C  (Fig.  103)  and  into  the  hole  in  the  plate. 
The  oil  will  be  drawn  to  the  parts  needing  lubrication  as 
the  pump  is  worked. 

The  edge  of  the  receiver  should  be  kept  scrupulously 
free  from  dust.  Before  placing  the  receiver  on  the  plate 
rub  its  edges  well  with  tallow,  then  put  it  into  position, 
pressing  it  downward  with  a  rotary  motion.  Renew  this 
rotary  motion  after  a  few  strokes  of  the  piston  to  be  sure 
of  an  air-tight  joint.  When  the  receiver  is  removed  from 
the  plate,  set  it  on  a  sheet  of  clean  paper. 

In  using  the  pump,  work  the  handle  up  and  down  as 
far  as  possible  with  a  motion  quick  but  steady  and  free 
from  all  jerking.  See  Pickering's  "Physical  Manipula- 
tion," p.  103. 

The  following  description  of  an  easily  made  air-pump, 
written  by  Mr.  Geo.  M.  Hopkins,  is  copied  from  the  Scien- 
tific American,  with  the  consent  of  its  publishers,  Munn 
&  Co.,  37  Park  Row,  N.  Y. 


[Elements  of  Natural  Philosophy;  p.  170.]  123 

The  engraving  (page  124)  shows  in  perspective  in  Fig.  1,  and  in 
section  in  Fig.  2,  an  air-pump  which  may  be  readily  made.  The  base, 
.Lis  a  perfectly  plain  board,  8  inches  wide,    1>  inches  long,  and 

1  inch  thick.  A  ■} -inch  hole  is  bored  longitudinally  through  the  cen- 
ter, and  near  one  end,  two  /,.  inch  holes  are  Ixm-d  into  the  longi 
tudiual  hole  at  a,  J  inch  apurt.  Another  ,^-iuch  hole  is  made  at  6, 
and  another  one  at  c.  The  board  may  be  of  any  well  seasoned  wood 
that  is  not  liable  to  warp.  Alter  boring,  it  should  receive  several 
x>ats  of  good  alcoholic  shellac  varnish  on  all  sides  and  in  the  holes. 
When  the  last  coat  is  applied,  a  G-inch  disk,  J,  of  elastic  packing 
rubber,  having  a  small  central  aperture,  and  crbich  has  p;eviously 
received  a  coat  of  the  same  kind  of  varnish,  is  placed  varnish  Bide 
down  upon  the  board,  with  its  central  aperture  coincident  with  the 
hole,  r,  in  the  board,  and  it  is  kept  in  position  under  slight  pressure 
until  the  varnish  dries,  which  will  take  a  considerable  time  (a  day 
or  so),  being  confined  between  the  two  surfaces.  To  the  base,  A, 
two  wooden  standards,  B,  are  secured,  each  6i  inches  high  and  about 

2  inches  wide  at  the  narrower  end  and  -*■  inch  thick.  They  are  two 
inches  apart,  and  are  connected  at  the  top  by  a  cross-piece,  G.  The 
base,  A,  standards,  B,  and  cross-piece,  C,  should  be  fastened  together 
with  long  screws.  The  pump-barrel,  I),  is  a  piece  of  glass  tubing  1 J 
inches  internal  diameter,  and  6  inches  long.  A  piece  which  is  as 
nearly  true  and  straight  as  possible  should  he  selected,  it  may  be 
cut  from  a  long  piece  by  turning  it  in  a  heated  loop  of  heavy  iron 
wire  which  half  encircles  the  tube.  The  tube  should  be  turned  back 
and  forth  at  first,  until  it  begins  to  crack,  When  it  should  be  turned 
slowly  round  in  one  direction  until  it  cracks  entirely  around.  If  the 
ends  need  to  be  squared  up,  they  may  be  readily  ground  upon  an 
ordinary  grindstone,  or  by  moving  it  with  ■  <ryratory  motion  upon  a 
slab  of  glass  having  upon  its  surface  some  coarse  emery  and  water. 
A  piece  of  mandrel-drawn  brass  tube  will  answer  as  a  barrel  equally 
well  as  the  glass  tube. 

The  lower  end  of  the  pump-barrel  rests  upon  a  soft  rubber  disk. 
E,  and  a  ring  of  the  same  material  is  placed  between  the  cross-piece, 
f\  and  the  upper  end  of  the  barrel.  The  rubber  disk,  E,  ha>:  an 
oblong  aperture,  also  a  small  circular  one,  as  seen  in  Fig.  .">.  The 
oblong  aperture  is  placed  over  the  right-hand  hole  at  a  ;  the  small 
aperture  over  the  left-hand  hole. 

A  disk,  F.  Fig.  4.  of  hard  rubber,  brass,  or  other  suitable  material, 
having  its  edge  grooved,  and  having  two  small  apertures  (,',,  loch), 
which  coincide  with  the  holes  at  a,  is  covered  on  its  under  side  with 
oiled  silk,  which  is  drawn  over  its  edges  and  fastened  by  a  stout 
thread  wound  in  the  groove.     Two  slits  are  cut  in  the  oiled  silk,  one 


124  [Elements  of  Natural  Philosophy,  p.  170.] 


[Elemi'iita  of  PkHowpkg,  p.  170.]  ir> 

upon  each  side  of  the  right-hand  hole,  making  a  valve  which  wort 
in  the  little  chamber  formed  by  the  oblong  hole  in  the  packing  disk, 
E\  the  oiled  silk  is  removed  around  the  left-hand  hole.  The  upper 
valve,  which  is  shown  in  V\g.  '•>,  consists  of  a  strip  of  oiled  silk. 
which  covers  the  left-hand  hole,  and  is  fastened  by  a  thread  arounc' 
the  edges  of  the  disk,  as  in  the  other  case. 

The  disk.  F,  is  placed  upon  the  packing  disk,  K,  and  secured  Lj 
four  small  screws  that  pass  through  both  into  the  base. 

The  piston,  I/,  Consists  of  two  disks  of  wood,  which  have  been 
in  melted  paraffin  to  prevent  them  from  absorbing  moisture. 
The  lower  one  nearly  fill  the  barrel  ;  the  upper  one  is  small  enough 
ceive  between  it  and  the  barrel  a  leather  packing,  which  is 
turned  upward  in  the  same  manner  as  the  packing  of  an  ordinary 
(4,in  pomp.  The  piston  is  fastened  to  the  end  of  the  wooden 
piston-rod,  I,  by  means  of  a  long  wood  screw.  The  piston-rod  i 
upward  through  a  hole  in  the  cross-piece,  C,  and  is  provided  with  a 
suitable  handle. 

A  rubber  stopper  is  forced  into  the  longitudinal  hole  in  the  bee 

sen  the  two  holes  at  a,  and  another  rubber  stoppei 

rite  end  of  the  hole.     An  oiled  silk  or  flexible  rubber 

flap  or  valve  covers  the  hole,  b.    The  piston  should  be  greased  with 

lard.    By  adding  to  the  piston  a  second  packing,  turned  downwaid 

the  pomp  may  be  used  for  the  compression  of  air. 

Any  of  the  experiments  performed  with  other  air-pumps  may  bs 
repeated  with  this.  A  bottomless  glass  jar  is  shown  in  the  present 
ipon  tin-  soft  rubber  disk,  J!  It  has  a  thin  piece  of  elastic 
rubber  stretched  over  its  mouth,  and  tied.  When  the  air  is  exhaust- 
ed, external  air-pressure  forces  the  elastic  rubber  downward.  By 
substituting  a  piece  of  bladder  for  the  rubber,  it  will  burst  with  a 
loud  report.  By  placing  the  hand  over  the  mouth  of  the  jar  and 
exhausting  the  air,  the  fact  that  the  air  has  weight  will  at  once  be 
realized.    [§  293,  (6.)  and  (7.).] 

A  strong  common  fruit-jar  may  be  used  as  a  receiver,  and  to  in 
sure  a  perfect  joint  with  the  rubber  disk,  a  packing-ring  of  very  soft 
rubber  may  be  interposed  between  the  mouth  of  the  jar  and  the  rub 
be?  disk,  J,  and  in  any  case  the  rubber  disk,  and  whatever  is  placed 
on  it,  should  b  •  greased  with  lard  to  make  a  joint. 

The  fountain  in  vacuo  [§  293,  (9.)]  requires  no  expensive  appa 
ratus.  All  that  is  n<  eded  is  a  small  tube  or  jet.  which  may  be  eithei 
of  metal  or  glass,  a  piece  of  stiff  rubber  tubing,  and  two  good  corks 
or  rubber  stoppers.  One  of  the  corks  is  Inserted  in  the  lw>tth-  sod 
the  jet  is  inserted  in  the  cork,  the  rubber  tube  is  slipped  over  the 


126 


[Elements  of  Natural  Philosophy,  p.  170.] 


outer  end  of  the  jet  tube  and  is  fitted  to  a  hole  in  the  second  coik, 
as  seen  in  Fig.  6. 

To  exhaust  the  air  from  the  bottle,  stop  the  hole,  c,  insert  the 
cork  that  is  on  the  end  of  the  rubber  tube,  in  place  of  the  stopper  in 
the  end  of  the  bed.  Work  the  pump,  and  when  the  air  is  exhausted 
bind  the  rubber  tube,  as  indicated  by  the  dotted  lines,  so  as  to  close 
it ;  raise  the  valve  from  the  hole,  b,  to  admit  air  to  the  passage  in  the 
bed,  and  remove  the  cork  on  the  rubber  tube  from  the  hole  in  the 
bed,  and  dip  it  in  a  vessel  of  water,  at  the  same  time  allowing  the 
rubber  tube  to  straighten  out. 

To  illustrate  the  principle  of  the  Magdeburg  hemispheres  (£  293, 
[13}).  make  a  ring  of  wood  a  little  larger 
than  <i  tumbler-top,  soak  it  in  melted 
paraflni,  attach  to  each  side  a  packing-ring 
of  ve»y  soft  rubber,  fasten  in  one  edge  a 
piece  of  rubber  tubing,  which  communi- 
cates with  the  interior  of  the  ring ;  place 
Dn  e^ch  side  of  the  ring  a  tumbler  with 
tts  mouth  in  contact  with  the  packing- 
ring  ;  exhaust  the  air  as  in  the  case  of  the 
fountain  bottle,  and  prevent  its  re-entrance 
by  bending  the  tube  short.  The  tumblers 
will  press  so  firmly  upon  the  ring  that  it 
will  be  difficult,  if  not  impossible,  to  sepa- 
rate them  from  it.     (See  the  annexed  cut.) 

It  is  not  necessary  to  enumerate  here 
ihe  many  interesting  experiments  that 
may  be  made  with  an  air-pump,  as  most  of  them  are  well  known, 

See  Frick's  "Physical  Technics/'  pp.  112,  113  and 
Deschanel's  "  Natural  Philosophy/'  p.  197  ;  also  the  Cata- 
logue of  0.  E.  McVay,  Cincinnati,  Ohio. 


[SUmenU  »/  Xahmil  Pkitotophy%  />    I  M 

§  289.     Air-pumps  of  the  better  class  are  provided  with 
manometers,  for  the  purpose  of  showing  the  degn 

exhaustion  attained  at  any  given  time.  The 
figure  shows  one  form  of  the  manometer.  Over 
a  mercury  batli  are  inverted  two  glass  tubes. 
The  tube  at  the  left  is  a  barometer-tube  (§278), 
with  a  Torricellian  vacuum  (§  274)  at  the  closed 
or  upper  end.  The  upper  end  of  the  tube  at 
the  right  is  connected  with  the  receiver  or  tube 
of  the  air-pump.  As  the  air  is  exhausted,  the 
mercury  rises  in  the  second  tube,  being  forced 
up  by  atmospheric  pressure.  When  the  vacuum 
in  the  receiver  is  as  perfect  as  the  Torricellian 
vacuum,  the  mercury  will  stand  at  the  Bflme 
height  in  the  two  tubes.  Of  course,  the  mer- 
cury cannot  rise  higher  in  the  second  than  in 
the  first  tube.  (§  275.)  When  the  mercury 
column  in  the  second  tube  is  -fo  of  an  inch  shorter  than 
that  in  the  first,  we  say  that  the  tension  of  the  residual  air 
has  been  reduced  to  fo  of  an  inch  of  mercury.  Such  an 
attachment  is  unsatisfactorily  represented  in  Fig.  103  of 
the  text-book.  In  the  air-pump  represented  on  page  61,  a 
more  compact  form  of  manometer  is  shown.  A  glass 
receiver,  M,  is  connected  by  a  stop-cock  with  the  tube  t 
Within  M  is  a  bent  tube,  closed  at  one  end,  and  a  lit tk 
more  than  half  filled  with  mercury.  The  length  of  the 
closed  arm  of  this  bent  tube  being  less  than  that  of  the 
barometer  column,  under  ordinary  atmospheric  pressure, 


128 


[Elements  of  Natural  Philosophy,  p.  170.] 


the  mercury  is  forced  to  the  top  of  the  closed  arm.  Aa 
exhaustion  proceeds,  the  pressure  upon  the  mercury  in  the 
open  arm  diminishes.  Soon,  the  tension  of  the  air  in  M 
becomes  too  feeble  to  support  a  column  of  mercury  equal 
to  the  vertical  distance  between  the  mercury  surfaces  in 
the  two  arms.  Then  the  mercury  begins  to  fall  in  the 
closed  arm  and  to  rise  in  the  open  one.  When  the  ex- 
haustion is  complete,  the  mercury  stands  at  the  same  level 
in  the  two  arms.  (§233.)  At  any  instant  after  the  mer- 
cury begins  to  move,  the  vertical  distance  between  the  two 
mercury  surfaces  measures  the  tension  of  the  air  in  M9  J?, 
and  t. 


[Elements  of  Natural  Philosopfty,  pp.  m-179.]  129 

§293.  See  Prick's  ■■  Physical  Ti-Hmifs/'  p.  119  (§17) 
and  Deschanel's  "Natural  Philosophy"  £S  109,  170,  174. 

Make  a  small  hole  (2  or  3  mm.  across)  in  the  small  end  of  an  egg. 
Place  the  egg,  perforated  end  downward,  in  a  wine-glass  so  that  the 
egg  shall  come  within  about  1  //////.  <»t*  the  bottom  of  the  glass. 
Place  the  glass  under  the  receiver  of  an  air  pump  and  exhaust  the 
air  therefrom.  The  tension  of  the  air  within  the  egg  will  drive 
some  of  the  contents  of  the  shell  into  the  wine  glass.  On  the  re- 
admission  of  air  to  the  receiver,  atmospheric  pressnre  will  generally 
drive  the  fluid  back  into  the  shell. 

Pass  a  glass  tube  through  the  stopper  of  a  good  sized  bottle. 
Slip  the  end  of  a  snugly  fltting  rubber  tube  over  the  outer  end  of  the 
glass  tube.  All  of  the  joints  should  be  air-tight.  Suck  as  much 
air  as  you  can  from  the  bottle,  pinch  Che  rubber  tube  close  and  place 
ii-  ebd  in  water.  On  releasing  the  tube,  atmospheric  pressure  will 
force  water  into  the  bottle.  If  the  inner  end  of  the  glass  has  been 
drawn  out  to  a  small  jet  (see  Mem.  Chemistry,  Appendix  4  [c]),  you 
will  have  a  pretty  little  fountain. 

§  298.  See  Frick's  "  Physical  Technics,"  p.  118  (§  14) 
and  p.  124  (§  104). 

Exercises,  I*€ige  179, 

1.  30  in.  x  13.6  ==  408  in.  =  34  ft— Ans. 

2.  28  ft.  ~  0.8  =  35  ft.— Ans. 

3.  (See  §  274.)  76  cm.  x  13.6  =  1033.6  cm.  =  10.336  m^ 
the  height  to  which  atmospheric  pressure  will  lift  water. 

(a.)  It  cannot,  because  atmospheric  pressure  is  not  suf* 
fkrieat  to  force  the  water  up  to  that  height. 


130  [Elements  of  Natural  Philosophy,  p.  180.] 

(b.)  The  same  as  for  (a). 

[c.)  It  can,  because  the  water  is  lifted  by  muscular  or 
some  similar  form  of  energy  not  subject  to  the  limitations 
placed  upon  atmospheric  pressure. 

4.  755  mm.  x  13.6  ~  2.96  —  3,468.9  mm. 

=  3.4689  m.—Ans. 

5.  34  ft.  -r-1.8  =  18.8+  ft,—  Ans. 

6.  15  lb.  x  15  =  225  lb.— Ans. 

7.  (a.)  See  §  289.     (*)*  =  £f§. 

(b.)  Iff  as  great.  (§  287.)  There  being  only  £f£ 
as  much  air  in  the  receiver  as  there  was  at  the  beginning, 
when  its  tension  was  the  same  as  that  of  the  external  air, 
its  density  and,  hence,  its  tension  is  only  -§-|f  as  great  as 
that  of  the  external  air.     See  §  62. 

8.  29.5  in.  x  13.6  -+-  1.35  =  223.11  in.— Ans. 

9.  69  cm.  x  13.6  =  938.4  cm.  =  9.384  m.—Ans. 

10.  (a.)  15  lb.  x  3.1416  x  22  =  188.496  lb.—  Ans. 
(b.)  1  Kg.  x  3.1416  x  42  =  50.2656  Kg.— Ans. 


Review  Questions,  Page  ISO. 

3.  (c.)   500  x  60  =  30000,  the  momentum. 

,'  x  w&       500  x  3600        OWrtOK  t      ,.  . 

(d.)  -—  =  — — — - —  —  27985+,  the  number  of 

iig  t>4:.0/S 

foot-pounds. 

Note. — A  modification  of  the  formula  given  in  §  157,  which  is 
often  a  practical  convenience,  may  be  obtained  as  follows : 

_  _        w&         I  u*  \  /  v  Y 

K-E-  =  ^=wW3)  =  wU:o2)- 

Using  this  formula,  the  solution  of  the  problem  above  is  as  follows : 
W  {mf  =  50°  {w&f  =  50°(7-481)2  =  500  x  55.965+  =  27982  + 
(e.)  Each  would  be  doubled. 


[Elements  of  Natural  Philosophy,  pp.  180-182.]  131 

(/.)  The  momentum  would  be  increased  twofold;  the 
eiu-rgy,  fourfold. 

4.  (c.)    See  §  106.    w  :  W  ::    IP  :  (P; 
90  :  1440    ::    40002  :  d*. 
d  =  1G000; 
16000  —  4000  =  12000,  the  number  of  miles  from  the  cen 
tre  of  the  earth. 

Or,  we  may  proceed  as  follows:  The  weight  is  to  be 
divided  by  16 ;  then  its  distance  from  the  centre  of  the 
earth  must  be  multiplied  by  (ViG  =  )  4.  If  its  distance 
from  the  centre  of  the  earth  is  to  be  4  times  the  radius  of 
the  earth,  its  distance  from  the  surface  of  the  earth  will  be 
3  times  the  radius  of  the  earth ; 

3  t»mes  4000  mi.  =  12000  ml 

(d.)  w  :  W   ::    d  :  D; 

w  \  T440    ::    (4000  —  2200)  :  4000. 
/.    w  —  648,  the  number  of  pounds. 
7.  J  of  39.1  he.  is  4.34+  in. 

Or,  i  of  9'<3.3  mm.  is  110.36+  mm.  =  11.036  cm. 

IT.  (2J)2  =  635;    39.1  in.  x  6.25  =  244.375  in. 

Or,  993.f,  mm.  x  6.25  =  6208.125  mm.  =  6.208125  m. 

13.  See  §  *»74,  and  the  solution  of  Prob.  34,  on  page  96 
n'  text-book.     (Page  84  of  Hand-book.) 

14.  <*)     v=zgthJ=^;eUi. 

(d.)    8  aa  yfl;     5280  =  16.08/2;     .-.  t  =  18.12. 
{e.)     v  =  gt;  v  =  32. 16  ft.  x  18.12  =  582.739  ft.  4  . 

B»  sure  that  the  pupil  understands  that  this  disregards  the  resist- 
tnce  of  the  air,  considering  tllf>  b,Kiy  as  a  /r,Y/y  fa]lin«r  body.  The 
resistance  of  the  air  would  make  a  very  considerable  difference  in  the 
**sult. 


132  \Elements  of  Natural  Philosophy,  pp.  1S0-182.~\ 

15.  (a.)     S  =  igt2  +  35t  = 

(16.08  x  12.5  x  12. 5)  +  (35  x  12.5)  = 
2950,  the  number  of  feet. 

(i.)     v=gt  +  3o  ft.  =  32.16  ft.  x  12 J  +  35  ft. =437  ft 

16.  (a.)     170  +  (7  x  20)  =  310  ; 

310  x  30  =  9300,  the  number  of  foot-pounds. 

(b.)     158100  -7-  9300  =  17,  the  number  of  trips  per 

day. 
20  bricks  x  17  =  340  bricks. 

18.  See  §  238.  The  body  will  displace  1  cu.  m.,  op 
1000  cu.  dm.  (which  is  only  another  name  for  1000  liters) 
of  each  gas. 

(a.)  See  Appendix  G.     One  liter  of  hydrogen  weighs 
.0896  g. ;  the  1000  liters  displaced  will  weigh 
.0896  #.  x  1000  =  Sd.6g.—Ans. 

(b.)  See  §  272.  One  liter  of  air  weighs  1.293  g. ;  the- 
1000  liters  displaced  will  weigh 

1.293  g.  x  1000  =  1293  g.  =  1.293  Kg.—Ans. 

(c.)  See  §  253,  (3.).  Carbonic  acid  gas  being  22  times  as 
heavy  as  hydrogen,  a  liter  of  it  weighs  22  times  .0896  #.> 
or  1.9712  g.    Then  a  cubic  meter  of  it  will  weigh 

1.9712  #.  x  1000  =  1971.2^.,  or  1.9712  Kg.— Am. 

19.  Place  it  under  the  receiver  of  an  air-pump.  The 
vertical  distance  from  the  level  of  the  mercury  in  the  bath 
to  that  of  the  mercury  in  the  tube,  measures  the  tension 
of  the  residual  air.  In  a  perfect  vacuum,  the  two  mer- 
cury surfaces  would  be  at  the  same  level. 

20.  See  §  231.     5x12x6  =  360,  the  number  of  cu.  ft 
in  the  imaginary  column  of  water. 

62.42  lb.  x  360  =  22471.2  lb.— Ans. 

22.  See  §  273.  "I  Kg.  to  the  sq.  cm."  16000  Kg.— Ans. 


[Elements  of  Natural  Philosophy,  pp.   180-18S.]  133 

23.  The  balloon  contains  1000000  liters  of  gas.  See 
§  11i.  That  much  uir  weighs  1.293  g.  x  1000000  = 
1000  g.  or  1293  Kg.  One  half  of  this,  or  646.5  Kg., 
represents  the  weight  of  the  gas  and  also  the  buoyant 
effort  of  the  gas.  From  this  buoyant  effort  of  646.5  Kg., 
subtract  the  weight  of  the  balloon. 

646.5  Kg.  —  25  Kg.  =  621.5  Kg.—Ans. 

8  1.  38  g.  —  28  g.  =  10  g.,  the  weight  of  an  equal  bulk 
of  water.  38  g.  —  20  g.  =  18  g.,  the  weight  of  an  equal 
bulk  of  acid.     18  g,  -f-  10  g.  =  1.8,  the  sp.  gr.  of  the  acid. 

26.  (c.)  To  bring  the  center  of  gravity  low,  and  thus  to 
increase  the  stability.     See  §  117. 

27.  The  volume  of  150  g.  of  water  is  150  cu.  an.  As  the 
lead  is  11  times  as  heavy  as  water,  the  volume  of  150  g.  ot 
iead  will  be  ^  of  150  cu.  an.,  or  13.63  cu.  cm.  The  lead 
will  displace  13.63  cu.  cm.  of  acid.  1  cu.  cm.  of  acid  weighs 
1.75  //.  (See  note  at  foot  of  page  141,  text-book.)  The 
acid  displaced  will  weigh  (1.75  g.  x  13.63  =)  23.8525  #. 
The  lead  will  weigh  in  the  acid  (150^.-23.8525^.  =) 
126.1475//.—  Ans. 

28.  It  is  to  vibrate  f-g-  or  f  times  as  fast.  Then  it  must 
be  (|)2  or  J  times  shorter,  or  $  as  long. 

$  of  1  m.  =  444. 4 -f  mm. — Am. 

29.  We  must  assume  the  perfect  pump.  If  atmospheric 
pressure  lifts  mercury  29.5  in.,  it  will  lift  water  13.6  times 
as  high,  or  401.2  in.     If  it  lifts  water  401.2  in.,  it  will  lift 

the  given  liquid  ~^  in.,  or  297.185  +  in. — Ans. 

30.  See  Fig.  102.     (e.)  The  tension  of  air  in  air-chamber. 

31.  r  =  8.02  a/A  =  8.02  x  5  =  40.1. 

S  =  igt* ;     144.72  =  16.08A    .-.  t  =  3. 
40.1  ft  x  3  —  120.3  ft.— Ans. 

32.  See  Recapitulation  on  page  24  of  text-book. 

Just  the  same.     In  either  case,  the  wood  is  0.9  as 
heavy  as  an  equal  hulk  of  water. 


CHAPTER  VI. 

§  302.  The  following  recipe  for  the  preparation  of  the 
amalgam  mentioned  in  sub-paragraph  (a),  is  said  to  be 
good: 

"  Melt  together  5  parts  of  zinc  and  3  parts  of  tin  and,  on  the 
melted  mixture  gradually  pour  9  parts  of  heated  mercury.  The 
whole  is  shaken  briskly  till  cold  in  an  iron  or  thick  wooden  box.  It 
is  then  finely  pulverized  in  a  mortar,  sifted  through  muslin  and 
mixed  with  sufficient  lard  to  form  a  paste.  This  paste  is  to  be 
spread  evenly,  and  any  excess  that  does  not  adhere  to  the  rubber 
should  be  wiped  off  with  paper." 

As  a  general  thing,  it  will  be  better  to  send  to  Jas.  W. 
Queen  &  Co.,  924  Chestnut  St.,  Philadelphia,  for  such 
supplies. 

§313.  "The  unsolved  question, '  What  is  electricity?'  we  shall 
not  attempt  to  touch  upon.  When  a  body  exhibits  certain  proper- 
ties, it  is  said  to  be  electrified.  We  know  how  to  produce, this  state 
at  will  but  we  know  next  to  nothing  of  its  nature.  *  *  *  We 
have  no  conception  of  electricity  apart  from  the  electrified  body  ;  no 
experience  of  its  independent  existence." 

The  above  is  from  pp.  3  and  4  of  J.  E.  H.  Gordon's 
"  Four  Lectures  on  Electric  Induction,"  published  by  D. 
Van  Nostrand,  N.  Y.  It  is  well  worth  while  to  get  this 
little  book.     See  Hand-Book  notes  on  §§  316,  352. 

§  315.  The  teacher  will  find  much  information  that  will 
be  of  immediate  value  to  him  in  Frick's  "  Physical  Tech- 
nics," pp.  253-310. 

§316.  "We  cannot  make  or  destroy  electricity.  We  can  only 
strain  bodies  so  that  their  two  ends  shall  show  opposite  electrical 


[Elements  of  Natural  PhVwtphy,  pp.   104-205.]  L35 

proprjttlML  When  we  rubbed  glass,  we  produced  positive  electricity 
on  its  surface.  Was  not  that  a  creation  of  electricity  '!  So  ;  for  an 
exactly  equal  amount  of  negative  electricity  was  produced  on  the 
rubber,  as  1  can  show  you.  (The  rubber,  on  being  laid  on  the  elec- 
troscope, caused  a  strong  divergence  of  the  leaves.)  To  show  that 
this  negative  is  equal  to  the  jx)sitive,  a  very  simple  experiment  will 
suffice.  I  rub  this  sealing-wax  till,  by  the  cracking,  you  can  hear 
that  it  is  highly  electrified,  but  I  do  not  remove  the  rubber  from  it. 
You  see  that  there  is  no  effect  on  the  electroscope." — Gordon. 

§  323.  When  we  wish,  not  merely  to  defect  electrifica- 
tion bnt  to  measure  it,  our  electroscope  will  not  answer  ; 
we  need  an  electrometer.  For  a  good  but  simple  explana- 
tion of  Sir  William  Thomson's  quadrant  electrometer,  see 
Gordon's  "  Electric  Induction,"  p.  35. 

(b.  See  Hand-Book  note  on  Review  Question  26,  p. 
411  of  text-book. 

§  332.  See  Hand-Book  note  on  §  653  of  text-book. 

"  Every  electrified  body  from  which  no  electrification  is  allowed 
to  escape  has  a  particular  action  on  all  neighboring  bodies  and  this 
action  is  called  induction." — Gordon. 

\  o  induction  can  take  place  through  a  metal  screen 
that  is  connected  to  the  earth  but  the  induction  may  act 
in  curved  lines  around  the  edges  of  the  screen,  if  the 
screen  be  small  and  the  inducing  charge  intense.  A  body 
surrounded  by  a  wire  cage  connected  with  the  earth  is 
thoroughly  protected  against  injury  by  lightning.  See 
(i onion's  "  Electric  Induction,"  p.  -41. 

§  334.  The  polarized  conductor  of  §  332  showed  —  elec- 
tricity at  the  near  end  and  +  at  the  far  end.  In  this  par- 
agraph  we  are  concerned  only  with  the  near  end. 

11  We  will  lengthen  our  cylinder  so  as  to  get  the  far  end  out  of 
our  way.  How  are  we  to  do  this?  This  is  a  large  room  (in  the 
Royal  Institution  of  Great  Britain)  and  no  doubt  we  might,  at  some 
( <>nsi(ler;ible  trouble  and  expense,  so  lengthen  the  cylinder  that  we 
could  remove  its  other  end  to  a  distance  of  some  twenty  <>r  thirty 
feet     But  we  can  do  better  than  that.     We  will  make  the  whole 


13 G  [Elements  of  Natural  Philosophy,  pp.  205-215.] 

world  part  of  our  conductor.  The  earth,  owing  to  the  water  in  it, 
is  a  good  conductor  (for  frictional  electricity).  We  will  connect  this 
wire  from  the  cylinder  to  the  water-pipes,  and  now  we  have  one  end 
of  our  conductor  on  the  table  and  the  other  safely  tfut  of  our  way 
somewhere  in  Australia." — Gordon.  , 

§  337.  It  will  be  better  if  teacher  and  pupils  studiously 
avoid  the  use  of  the  expression  "electrical  fluid''  and  use, 
instead,  the  less  misleading  word  "  electricity."  If  the 
teacher  wish  to  refresh  his  memory  concerning  the  old 
"one-fluid"  and  "two-fluid"  theories  of  Franklin  and 
Dufaye,  he  may  refer  to  DeschaneFs  "  Natural  Philosophy," 
§  411,  A. 

§  341.  See  DeschaneFs  "Natural  Philosophy,"  §  421,  B. 

§342.  See  DeschaneFs  "Natural  Philosophy,"  §§  421, 
D;   416;  422;  424;  425. 

§  343.  Cottrell's  Rubber  is  a  very  simple  electric 
machine.     It  is  thus  described  by  Dr.  Tyndall  : 

"  A  strip  of  sheet  brass  or  copper  is  sewn  on  to  the  edge  of  the 
silk  pad  employed  as  a  rubber.  Through  apertures  in  the  strip, 
about  twenty  pin  points  are  introduced  and  soldered  to  the  metal. 
When  the  tube  is  clasped  by  the  rubber,  the  metal  strip  and  points 
quite  encircle  the  (glass)  tube.  When  a  fine  wire  connects  the  strip 
of  metal  with  the  knob  of  a  Leyden  jar,  by  every  downward  stroke 
of  the  rubber,  the  glass  tube  is  powerfully  excited,  and  hotly  fol- 
lowing the  exciting  rubber  is  the  circle  of  points.  From  these, 
against  the  rod,  negative  electricity  is  discharged,  the  free  positive 
electricity  escaping  along  the  wire  to  the  jar,  which  is  thus  rapidly 
charged." 

For  a  description  of  Armstrong's  hydro-electric  machine 
(for  the  developing  of  electricity  by  the  friction  of  steam 
against  the  sides  of  orifices  through  which  it  is  allowed  to 
escape  under  high  pressure),  see  DeschaneFs  "  Natural 
Philosophy,"  §  431.  Many  other  forms  of  electric  ma- 
chines are  described  in  the  same  chapter. 

Of  the  late  forms  of  electric  machines,  the  Wimshurst 
machine  is  spoken  of  as  being  very  simple  and  very  efficient. 


[Element*  of  Natural  Philosophy,  pp.  215-222]  137 

Full  particulars,  as  to  cost,  etc,  may  be  had  by  addressing 
Jas.  \Y.  Queen  &  Co..  Philadelphia.  If  the  teacher  or 
pupil  has  skill  in  the  use  of  tools,  he  may  easily  make  one. 
Full  directions,  including  illustrations  and  working  plans, 
are  given  in  the  "  English  Mechanic "  for  Oct.  1G,  1885 
(No.  1073).  Any  bookseller  can  get  the  paper  for  you  for 
a  dime  or  two.  An  explanatory  article  on  the  same  machine 
may  be  found  in  the  "English  Mechanic "  for  January  12, 
1883,  or  "  The  Electrical  World,"  June  12,  1886. 

See  note  in  text-book  following  §  349.  Always  keep 
school  (especially  electrical)  apparatus  in  a  dry,  well  venti- 
lated room.  Protect  the  electric  machine,  when  not  in 
use,  with  a  cover  of  woolen  cloth.  In  placing  the 
machine  by  a  stove  to  warm  it,  turn  the  edge  (not  the  side) 
of  the  plate  toward  the  fire.  The  plate  maybe  cleaned 
with  a  woolen  cloth  moistened  with  turpentine  and  then 
thoroughly  rubbed  with  a  clean,  dry,  warm  cloth.  If  con- 
venient, connect  the  negative  conductor  to  a  gas  or  water- 
pipe  when  the  machine  is  to  be  used.  Keep  the  class  back 
a  little  ways  from  the  machine  that  the  instrument  may 
not  be  moistened  by  their  breath. 

§  347.  If  you  have  a  dielectric  machine  (Fig.  143),  set 
it  in  action  and,  while  a  steady  stream  of  sparks  is  passing 
between  the  prime  conductor  and  the  discharging  knob, 
press  the  finger  gently  against  the  lower  part  of  the  upper 
plate  (near  the  lower  comb).  It  has  no  effect  upon  the 
series  of  sparks.  Press  the  finger  upon  the  plate  near  the 
upper  comb.  Notice  that  the  sparks  cease.  Press  the 
finger  upon  the  upper  part  of  the  lower  plate.  The 
sparks  cease.  The  first  contact  did  not  affect  the  series  of 
sparks,  because  it  made  no  difference  whether  the  repelled 
—  electricity  of  the  plate  A.  e*  aped  by  the  lower  comb 
or  through  the  human  body.  The  second  contact  canted 
a  cessation  of  sparks,  because  (he  free  -f  electricity  of  the 
plate,  A.  at  that  point  was  thus  neutralized  by  the  —  I ■!■  ■<  - 
tricity  from  the  finger.     Being  neutralized,  it  could  not 


138  [Elements  of  Natural  Philosophy,  p.  222.] 

polarize  the  upper  comb  and  prime  conductor.  The  third 
contact  had  a  similar  effect,  because  the  —  electricity  of 
the  plate,  B,  being  thus  neutralized,  could  exert  no  in- 
ductive effect  upon  the  plate,  A. 

Exercises,  Page  222. 

1.  See  Exp.  22,  p.  194. 

2.  See  §  322. 

4.  Because  they  produce  opposite  effects  when  presented 
to  a  third  charged  body.     See  §  322  and  Exp.  22. 

5.  That  it  may  not  condense  moisture  from  the  atmos- 
phere.    See  §  324. 

6.  (b.)  Induction,     (c.)  Opposite. 

7.  (a.)  Because  the  violent  repulsion  of  the  similarly 
charged  leaves  might  tear  them,  the  charge  being  too 
strong,  in  such  a  case. 

(Z>.)  The  gold  leaves,  the  brass  wire  and  the  knob  or 
plate  of  the  electroscope  form  one  continuous  conductor, 
insulated  from  other  objects  by  the  glass  jar.  For  the 
purpose  of  this  explanation,  we  may  assume  that  the  elec- 
trified body  held  in  the  hand  is  charged  positively.  The 
-f  electricity  of  such  a  body  acts  inductively  on  this  insu- 
lated conductor,  developing  —  electricity  at  the  near  end 
or  on  the  knob  and  +  electricity  at  the  far  end  or  on  the 
leaves,  which  then  diverge.  Of  these  two  separated  elec- 
tricities (§  332),  the  —  on  the  knob  is  "bound"  while  the 
-j- on  the  leaves  is  "free"  (§351).  When  the  knob  of 
this  polarized,  insulated  conductor  is  touched  by  an  unin- 
sulated body,  the  "free"  -f  electricity  of  the  leaves  escapes 
to  the  ground  and  the  leaves  fall  together.  The  —  elec- 
tricity is  still  "bound"  at  the  knob,  by  the  attraction  of 
the  inducing  body  and  can  not  affect  the  leaves.  But 
when  the  inducing  body  is  removed  from  the  immediate 
neighborhood  of  the  electroscope,  the  —  electricity,  hith- 
erto "bound,"  becomes  "free"  and  diffuses  itself  over  the 
insulated  conductor  of  which  we  have  spoken.     Part  of 


[Elements  of  Natural  Philosophy,  p.  223.]  130 

the  charge  passes  to  the  leaves  which  now  diverge  again, 
but  this  time  as  the  result  of  a  —  electrification. 
(c.)  It  is  — ,  as  explained  above. 

10.  Refer  to  Figure  133.  Let  C  represent  the  prime 
conductor  and  AB,  the  insulated  globe.  Ah  is  polarized 
by  the  iDductive  influence  of  C\  the  repulsion  of  the  + 
electricity  at  B  partly  counterbalances  the  attraction  of 
the  nearer  —  electricity  at  A,  and  the  resultant  action 
across  the  intervening  insulating  air  is,  consequently, 
feeble.  When  the  globe  is  held  in  the  hand,  the  repelled 
4-  electricity  at  B  escapes  and  no  longer  acts  in  opposition 
to  the  attraction  of  the  —  at  A.  The  mutual  attraction 
between  the  opposite  electricities,  being  now  unopposed, 
more  easily  overcomes  the  resistance  offered  by  the  inter- 
vening air. 

11.  Electroscope. 
12   See  §319  (1). 

13.  Since  the  charges  are  of  opposite  signs,  the  force 
will  be  attractive  and  not  repel  Ian  t.     See  §  319  (2). 

8xg_24x8_ 

Our  units  are  all  C.  G.  8.  units.  By  recognizing  the 
algebraic  signs,  we  have 

±^=^  =  -  n, 

which  also  indicates  an  attractive  force.     See  §  321  (a), 

14*  The  —  8  units  will  neutralize  an  equal  number  of 
the  -f  units,  leaving  -f  1<;  units  to  be  equally  divided 
between  the  two  balls  (which  are  assumed  to  be  of  equal 
capacity). 

f  -  <L?JL  -  8  x  8  _  ± 

J  -   (i*  "  4*  -:  ;*■ 

As  the  algebraic  sign  of  the  answer  is  -f-  (the  charges 
being  alike),  the  :  me  of  repulsion. 


140  [Elements  of  Natural  Philosophy,  pp.  :?26-228.] 

§  352.  "  In  the  two  previous  lectures,  we  have  seen  that  induction 
is  transmitted  from  particle  to  particle  of  dielectrics,  and  that  its 
phenomena  are  exhibitions  not  of  some  direct  action  passing  through 
the  insulator  but  of  something  actually  existing  in  the  particles  ot 
the  insulator  itself  ;  that  it  is  in  some  peculiar  straining  of  these 
particles  that  the  causes  of  the  phenomena  will  be  found." — Gordon's 
"  Electric  Induction,"  p.  tfj. 

"  Every  new  investigation  points  to  a  close  connection  between 
electricity  and  light.  The  theory  of  their  connection  requires  a  cer- 
tain relation  between  the  specific  induction  capacities  and  certain 
optical  properties  of  transparent  bodies.  This  theory,  which  may 
even  tell  us  what  electricity  is,  can  be  tested  only  by  an  accurate 
knowledge  of  the  specific  inductive  capacity  of  transparent  bodies." 
— Gordon's  "Electric  Induction," p.  63. 

The  third  of  the  four  lectures  that  constitute  the  book 
from  which  the  above  quotations  are  made,  gives  a  descrip- 
tion of  the  method  by  which  specific  inductive  capacities 
are  determined.     See  Hand-Book  note  on  §  360. 

§  353.  Leyden  is  pronounced  Liden.  Two  Leyden  jars 
have  equal  capacities  if,  when  their  knobs  are  electrically 
connected  and  their  outer  coatings  are  in  communication 
with  the  earth,  a  charge  given  through  the  knobs  divides 
itself  equally  between  the  jars.  If  twice  as  great  a  charge 
goes  to  jar,  A,  as  goes  to  jar,  Z?,  the  capacity  of  A  is  twice 
that  of  B. 

See  Deschanel's  "Natural  Philosophy,"  §§  447,  448. 

"  Charge  a  jar  from  the  prime  conductor  of  an  electrical  machine 
and,  rubbing  the  ball  over  the  resinous  surface  of  an  electrophorus. 
or  a  plate  of  glass  covered  with  shellac,  draw  a  figure  on  its  surface. 
Charge  another  jar  from  the  negative  conductor  of  the  machine  and 
draw  another  figure  across  the  first  figure.  Sift  the  dust  of  a  mixed 
po-.vder  composed  of  red  lead  and  sulphur  over  this  surface.  The 
two  powders  will  separate  and  arrange  themselves  in  beautiful  radia- 
ti  >ns,  the  red  lead  along  the  lines  formed  by  the  negative  jar  and 
the  sulphur  along  the  lines  formed  by  the  positive  jar." — Gage. 

§  354.  If  the  person  charging  the  jar  hold  it  by  the  knob 
and  present  the  outer  coat  to  the  charging  body,  the  jar 


[Elements  of  Natural  Phil>mphy.  pp.  228-232.]  141 

will  be  discharged  tli rough   his   person  when  he  ■ 
down  on  an  ordinary  table.     The  jar,  thus  charged,  should 
iirst  be  placed  on  an  insulated  support  and  tken   taken  by 
the  outer  coat  in  the  usual  way. 

The  "cascade"  method  of  charging  jars,  in  which  a 
number  (»)  <>f  similar, uncharged  jars  are  joined  in  settee, 
the  outer  coating  of  the  first  being  in  metallic  connection 
with  the  knob  of  the  second,  and  so  on,  and  the  ! 
then  charged  as  if  it  were  a  single  jar,  was  devised  by 
Benjamin  Franklin.  In  this  case,  the  difference  of  po- 
tential (  V)  between  the  outer  coating  of  the  last  jar  and 
the  knob  of  the  first  will  be  the  same  as  that  of  one  of  the 
same  jars  charged  by  itself  while  that  of  one  jar  of  the 

y 
series  will  be  —  .    This  arrangement  is,  therefore,  not  as 

N 

good  as  a  single  jar  fully  charged  by  the  same  machine. 
See  Hand-Book  note  on  Ex.  10,  p.  252,  of  the  text-book. 

§  355.  The  outer  coat  being  charged  with  u  bound  " 
electricity  by  the  inductive  influence  of  the  inner  coat, 
when  it  is  touched  by  the  discharger,  the  discharger  is 
also  charged  in  the  same  way  without  loss  of  intensity.  If 
me  discharger  be  iir.st  brought  into  contact  with  the  knob, 
the  —  electricity  of  the  discharger  will  be  attracted  by 
the  -f  of  the  inner  coat,  which  will  thus  be  partly  neutral- 
ized.    The  intensity  of  the  charge  would  thus  be  weakened. 

On  the  effect  of  electricity  upon  the  volume  of  bodies, 
see  Il'ir/xr's  M<t<i<tzinr.  March,  1879,  page  033. 

§  350.  See  Gordon's  u  Electric  Induction."  pp.  20-39. 

§  359.  The  pupil  may  remember  that,  in  §  330.  it  was 
said  that  "a  sphere  of  one  centimeter  radius  has  unit 
capacity''  and  wonder  why  it  is  now  said  that  a  farad  con- 
denaer  "would  be  too  lar  •  constructed.''    It  is 

necessary  only  to  point  out  that  the  nameless  unit  men- 
tioned in  §  330  is  an  electrostatic  unit  and  that  the  farad 
' ''  unit  derived  from  the  absolute  electro- 
magnetic unit  iribed  in  §§  451,  452.     The  electro- 


142  [Elements  of  Natural  Philosophy,  pp.  232-240.) 

magnetic,  unit  of  capacity  equals  9  x  1020  electrostatic 
units  of  capacity.  But  the  farad  is  10~9  of  an  electrostatic 
unit  of  capacity  and,  therefore,  equals  (9  x  1020  x  10~9  =±) 
9  x  1011  electrostatic  units  of  capacity.  As  the  electrostatic 
capacity  of  a  sphere  is  equal  to  its  radius  in  centimeters 
(§  330),  the  farad  equals  the  electrostatic  capacity  of  a 
sphere  having  a  radius  of  9  x  1011  cm.  Certainly,  "  such  a 
condenser  would  be  too  large  to  be  constructed."  See 
Hand-Book  note  on  §  452. 

§  360.  "  The  speed  of  signalling  and,  with  it  of  course,  the  gross 
receipts  of  the  telegraph  company  depend,  among  other  things,  on 
the  specific  inductive  capacity  of  the  cable  insulator.  The  lower 
the  specific  inductive  capacity,  the  greater  the  speed.  The  great 
object  of  telegraph  engineers,  at  present,  is  to  discover  a  good  insu- 
lator of  very  low  specific  inductive  capacity." — Gordon. 

Thus  does  pure  science  hold  up  the  arms  of  applied 
science. 

§  369.  The  "  Thunder  House  "  represented  in  the  figure, 
affords  a  striking  illustration  of  some  requirements  of  the 
lightning-rod.    The  house  may  be  held  together  by  magnets. 


The  rod  has  a  break,  arranged  so  that  if  it  is  closed,  the 
spark  passes  harmlessly  through  the  rod  ;  but  lr  it  is 
turned,  the  spark  passes  through  a  gas  pistol  placed  within 
and  the  house  is  thrown  down.  See  Exp.  58,  p.  244,  and 
Hand-Book  note  on  §  332. 

§  371.  In  Exp  39,  the  upper  plate  becomes  charged  by  the  direct 
action  of  the  machine.  The  images  are  then  polarized,  attracted  to 
the  upper  plate,  charged,  repelled,  discharged,  polarized,  attracted, 
charged,  repelled,  etc.,  etc. 


[Element*  of  Natural  Philosophy,  pp.  2Jfit  2*1.]         L43 

The  explanation  of  Exp.  41,  is  like  that  of  Exp.  8ft,  the  outer 
bells  being  in  the  place  of  the  upuer  plate  and  the  clappers  in  the 
place  of  the  images.  In  Exp.  42,  the  bell  on  the  jar  is  in  the  place 
of  the  upper  plate  of  Exp.  39  or  the  outer  bells  of  Exp.  41.  Modify 
the  experiment  by  bending  a  strip  of  tin  at  a  right-angle  so  that 
when  a  common  Leyden  jar  stands  on  the  horizontal  arm  of  the  tin, 
the  vertical  arm  may  reach  to  the  level  of  the  top  of  the  knob  of  (be 
jar.  Hang  a  pith -ball  by  a  silk  thread  so  that  it  may  vibrate  betw  ■<  •  i> 
the  knob  of  the  jar  and  the  tin  strip,  gradually  discharging  the  jar. 

See  Exp.  96,  First  Prin.  Nat.  PhV. 

In  Exp.  43.  one  of  the  knobs  is  in  place 
of  the  upper  plate  of  Exp.  39.  The  swinging 
image  takes  the  place  of  the  dancing  image. 
The  "  electric  see-saw,"  represented  in  the  ac- 
companying figure,  is  a  pretty  modification 
of  the  "swing"  and.  like  it,  is  easily  made 
by  an  interested  teacher  or  pupil.  The  three 
pillars  are  insulators  (glass  tubing  or  sealing-wax),  the  two  outer 
ones  being  connected  respectively  with  the  prime  conductor  and' 
the  earth,  or  with  the  two  coats  of  a  charged  Leyden  jar. 

In  Exp.  44,  the  inner  coat  of  the  jar  is  charged  by  conduction 
and  then  polarizes  the  outer  coat  and  the  pupil.  In  Exp.  5,  the 
pupil  was  charged  by  conduction. 

The  phenomena  of  successive  polarization,  attraction  and  repul 
sion  are  illustrated  by  the  following  interesting  experiments  : 

Float  a  small  metal  swan  upon  water  in  a  glass  or  other  insulating 
vessel.  Connect  the  water  with  the 
prime  conductor  of  an  electric  ma- 
chine in  action,  as  shown  in  the 
figure.  The  swan  thus  becomes 
charged.  Bring  an  extended  finger 
near  the  swan.  The  finger  becomes 
oppositely  charged  by  the  inductive 
action  of  the  swan.  On  account  of 
the  attraction  between  these  opposite  electricities,  the  bird  will 
follow  the  finger  in  any  direction,  as  far  as  it  can  float 

From  cork  or  pitch,  carve  the  body  of  a  large  spider  and  attach 
to  it  eight  linen  threads  (each  about  an  inch  and  a  half  long)  for 
legs.  By  a  silk  thread,  suspend  the  spider  between  the  knobs  of 
two  Leyden  jars  opjKisitely  charged.  It  will  vibrate  between  the 
two  knobs,  clasping  them  in  succession  with  its  legs  as  if  for 
support.     See  First  Prin.  Nat.  Phil.,  Exp.  97. 


144  [Elements  of  Natural  Philosophy,  pp.  241,  242.] 

In  Exp.  45,  the  thread  is  a  good  conductor  for  electricity  of  high 
potential.  The  kite  and  prime  conductor,  being  similarly  charged, 
repel  each  other. 

In  the  bottom  of  a  small  tin  pail,  pierce  a  few  holes,  so  fine  that 
water  from  the  pail  will  escape  from  them  only  drop  by  drop.  Sus- 
pend the  pail  from  the  prime  conductor ;  work  the  machine  ;  the 
water  escapes  in  small  streams  ;  electric  repulsion. 

In  Exp.  46,  the  divergence  of  the  strips  is  due  to  the  mutual  re- 
pulsion between  bodies  similarly  charged.  Concerning  the  phenom- 
enon next  mentioned,  see  §  336.  The  blowing  away  of  the  strips 
depends  upon  the  principle  stated  in  §  342.  The  air- particles  at  the 
point  of  the  needle  receive  a  charge  from  the  point  and  are  repelled, 
thus  producing  a  wind.  When  held  below  the  divergent  strips,  the 
—  electricity  of  the  air-particles  neutralizes  the  +  of  the  strips.  If 
you  have  time,  make  a  similar  tassel  of  cotton  or  linen  thread  and 
repeat  the  experiment.  The  tassel  is  easily  made  by  winding  the 
thread  around  a  cylinder  (as  a  fruit-can),  cutting  across  the  threads 
and  tying  them  together  in  the  middle  with  another  piece  of  thread. 
Instead  of  such  a  tassel,  the  hair  of  a  doll's  head  may  be  easily  pre- 
pared for  the  experiment ;  or  the  doll  (like  all  of  these  pieces  of 
apparatus)  may  be  bought  of  Jas.  W.  Queen  &  Co.  See  page  v.  of 
text-book.  Place  the  doll  upon  the  prime  conductor,  and  work  the 
machine.     See  Exp.  100,  First  Prin.  Nat.  Phil. 

In  Exp.  47,  the  leaves  were,  at  first,  polarized  by  induction.  After 
the  needle-point  was  uncovered,  they  were  charged  by  convection. 
See  Exp.  36  and  §  363. 

In  Exps  48  and  49,  the  principle  is  the  same.     It  is  to  be  noticed 
that  the  motion  here  produced  is  not  fully  explained   by  the  third 
law  of  motion.     (§§  72,  264 )    The  air- 
particles,  when  repelled,  exert  direct 
action  (repulsion)  as  well  as  reaction. 

The  adjoining  figure  represents  the 
"  Phosphorus  cups."  The  two  insu- 
lated cups  contain  bits  of  phosphorus. 
Between  them  is  a  lighted  candle. 
One  cup  communicates  with  the  earth  ; 
the  other  with  the  prime  conductor. 
When  the  machine  is  worked,  the  flame 
of  the  candle  is  blown  from  one  cup  toward  the  other.  The  phos- 
phorus in  the  second  cup  will  be  ignited,  while  that  in  the  first  is 
not.  Notice  the  direction  of  the  flame,  whether  it  is  deflected  by 
the  +  or  —  current.  Reverse  the  connections  and  repeat  the 
experiment. 


[Elements  of  Natural  Philosophy,  pp.  24s,  243.] 


Ub 


The  "electric  inclined  plane,"  represented  in  the  figure,  is  another 
modification  of  the  "  electric  whirl."  The' 
four  pillars  are  insulators.  The  wheel, 
axle,  and  inclined  bars  are  of  metal. 
When  either  of  the  bars  is  connected  with 
the  prime  conductor  and  the  machine 
is  worked,  the  wheel  rolls  up  hill. 

If  a  Leyden  jar  be  supported 
nppo  a  pane  of  glass  or  other  insulator,  it  can  receive 
only  a  feeble  charge.  (§  354,  a.)  If,  while  thus  insu 
lated,  its  outer  coat  be  provided  with  a  circle  of  points,  as 
shown  in  the  figure,  the  jar  may  be  more  fully  charged. 
Hero  again  we  see  illustrated  the  important  influenee 
exerted  by  pointed  conductors.  The  jar  may  be  pre- 
pared by  thrusting  sharp  pointed  tacks  through  a  narrow 
strip  of  leather  and  binding  the  strip  around  the  jar  so 
thiit  the  heads  of  the  tacks  shall  press  against  the  outer 
coat. 

In  Exps.  50  and  51,  we  have  simply  the  principle  of  the  Leyden 
jar.     The  water  in  the  beaker  and  the  insulated  pupil,  respectively 
represent  the  inner  coat  of  the  Leyden  jar.     The  glass  beaker  and 
the  India-rubber  cloth  respectively  represent  the  glass  jar.     The 
water  in  the  outer  vessel  and  the  uninsulated  pupil,  being  in  « -lee- 
Irical  communication  with  the  earth,  respectively  represent  the  outer 
coat  of  the  jar.     When  the  two  coatsof  any  of  these  modified  forms  of 
the  Leyden  jar  are  connected  by  a  person,  a  shock  is  felt.     (§  409.) 
After  i>erforining  Experiment  53,  try  the  following  : 
Charge  the  M  hand -jar,"  as  described  in  Experiment  51.     Let  the 
insulated  pupil  bring  a  metal  ball  suspended  from  his  hand  by  a  wet 
string,  over  some  gunpowder  on  a  metal  plate  having  a  good  con- 
n. ction  with  the  earth.     The  spark  will  ignite  the  powder. 
"  Kinnersley's  Thermometer,"  represented  in  the  figure, 
-ts  of  two  communicating  glass  tubes  of  unequal 
diameters.      The   smaller  one   is  open  at  the  top;   the 
larger  one  is  closed  at  both  ends.     Rex  Is  terminating  in 
knobs  pass  through  the  ends  of  the  larger  tube.     Both 
tubes  are  filled  with  alcohol  to  a  level  a  little  below  the 
lower  knob.     When  a  spark  is  made  to  pass  between  the 
two  kaobfl   r;'«  liquid  is  thrown  with  great  violence  from 
the  open  end  of  the  smaller  tube.     The  name  of  the  ap- 
paratus is  due  to  the  fact   that   Kinnersley  attributed  the 
in  . venu  ut    of  the    liquid    to  the   high  temperature    produced    by 
the  spark- 


146  [Memento  of  Natural  Philosophy,  pp.  248,  249.] 


In  Experiment  67,  tlie  sparks  seem  to  be  simultaneous,  because  of 
the  great  velocity  of  electricity.  They  are,  of  necessity. 
successive,  but  our  knowledge  of  their  being  successive 
is  a  result  of  the  action  of  reason  and  not  of  the 
senses. 

The  "  diamond  jar,"  represented  in  the  figure,  is  a 
modification  of  the  Leyden  jar.  The  two  coats  are 
made  of  diamond-shaped  or  square  pieces  ot  tin-foil, 
each  having  a  round  hole  in  its  middle.  These  bits  are 
placed  so  that  their  corners  do  not  quite  touch,  the 
corners  of  the  pieces  of  the  inner  fcoat  being  visible 
through  the  round  holes  in  the  pieces  of  the  outer 
coat.  When,  in  a  dark  room,  the  jar  is  charged  in  the 
usual  manner,  the  sparks  passing  from  corner  to  corner  of  the  pieces 
of  both  coats,  present  a  beautiful  appearance. 

Experiment  69. — The  appearance  of  the  spark  is  greatly  changed 
by  reducing  the  tension  of  the  ur  in  which  it  is  produced.  The 
accompanying  figure  represents  aii  oval  glass  vessel,  which  may  be 
exhausted  by  an  air-pump.  The  cap  at  the  upper  end  carries  a 
sliding  rod  terminating  in  a  knob,  which  may  be 
placed  at  a  varying  distance  from  another  knob  con- 
necting with  the  cap  at  the  lower  end.  The  upper 
knob  is  to  be  connected  with  the  positive  conductor  of 
an  electric  machine  ;  the  lower  knob  with  the  nega- 
tive conductor  or  with  the  ground.  As  a  series  of 
sparks  is  passing  between  the  knobs,  exhaust  the  air. 
At  first,  the  sparks  will  have  the  ordinary  appear- 
ance, but  as  the  tension  of  the  confined  air  is  dimin- 
ished, they  change  their  aspect. 
When  the  tension  is  reduced  to 
about  6  em.  of  mercury,  a  sheaf 
of  rays  of  violet  light  with  a 
reddish  tinge  seems  to  proceed 
from  the  positive  to  the  negative 
knob.  The  light  at  the  positive 
knob  is  reddish  purple  ;  that  at 
the  negative  is  violet.  When  the  exhaustion 
is  nearly  complete,  the  rays  become  less  dis- 
tinct and  blend  into  an  egg-shaped  cloud  cf 
pale  violet,  reaching  from  knob  to  knob.  The 
tube  used  for  bodies  falling  in  a  vacuum  (Fig. 
26),  is  often  adapted  for  a  similar  experiment 
In  this  case,  the  upper  rod  terminates  in  a  point  instead  of  a  knobv 


[Element*  of  Natural  Philosophy,  pp.  249-?:,:.]  147 

The  accompanying  figure  represents  "  Gassiot's  Cascade,"  which 
consists  of  a  glass  vase,  with  the  lower  part  of  the  inner  surface 
coated  with  tiu-foil,  and  a  capped  bell  -glass  provided  with  asliding- 
rod.  The  vase  and  the  bell-glass  are  placed  upon  the  plate  of  an  air- 
pump,  the  receiver  exhausted,  and  the  inner  surface  connected  by 
means  of  the  sliding  rod  with  the  prime  conductor.  A  beautiful 
light  seems  to  fill  the  vase  and  overflow  upon  the  plate  of  the 
air-pump.     The  effect  is  very  brilliant  in  a  dark  room. 

h\r/l('ii/tnit  ?o.  —  See  Deschanel's  "Natural  Philosophy,"  §618 
and  Plate  II  (colored)  in  the  same  bouk. 

For  the  method  of  producing  LicMenberg's  Figures,  see  Deschanel's 
"  Natural  Philosophy,"  §  462. 

Eacercises,  Bage  252. 

1.  Nothing.  §  341.  See  Faraday's  lath  cage  experi- 
ment, §  341  (b). 

2.  (a.)  See  §  351.  (b.)  The  outer  coat  is  polarized,  not 
charged.  The  -f  electricity  of  the  outer  coat  can  not 
escape.  The  +  electricity  of  the  outer  coat  repels  the  -f 
of  the  inner  coat  about  as  much  as  the  —  electricity  o! 
the  outer  coat  attracts  it.  Thus  there  is  but  little  u  con- 
densation." 

3.  (a.)  See  §§  341,  342.  An  unpolished  surface  presents 
a  multitude  of  little  protuberances  that  act  as  pointed  con- 
ductors, (b.)  See  the  Leyden  jar  with  circle  of  points, 
p.  145  of  Hand-Book. 

5.  (a.)  See  §  356. 

6.  (a.)  See  Fig.  134.  Place  the  dozen  globes,  M9  iV,  etc., 
in  actual  contact  They  will  be  polarized  as  a  single  body, 
and  may  all  be  charged  as  described  in  §  334.  (b.)  Charge 
one  negatively  by  induction  ;  with  it,  charge  another  posi- 
tively by  induction. 

7.  Connect  the  knob  of  the  first  and  the  prime-conductor; 
the  outer  coats  of  the  first  and  second  ;  the  knobs  of  the 
second  and  third ;  the  outer  coats  of  the  third  and  fourth  ; 
the  knob  of  the  fourth  and  the  ground.  Figure  such  an 
arrangement,  indicating  by  the  signs  +  and  — ,  the  elec- 
trical condition  of  each  coat  of  each  jar. 


148  [Elements  of  Natural  Philosophy,  p.  252.~\ 

8.  See  Exp.  29,  p.  212. 

9.  See  §  319  (2). 

;     _       28  x  56 
Whence,  d»  =  -^  =  49. 

10.  In  passing  from  the  outer  coating  of  the  last  jar,  at 
zero  potential,  to  the  knob  of  the  first  jar,  the  difference  of 
potential  will  be  n  times  the  difference  of  potential  be- 
tween the  two  coats  of  any  one  jar,  n  representing  the 
number  of  jars.  Compare  §  399  (a).  Where  great  elec- 
tromotive force  is  desired,  this  arrangement  has  great 
advantages  over  the  same  number  of  jars  placed  "  abreast," 
as  shown  in  Fig.  152.  For  instance,  the  striking  distance 
(see  next  Exercise)  is  much  greater. 

11.  See  the  preceding  note. 

12.  By  bringing  the  charged  conductor  into  simultaneous 
contact  with  two  similar  conductors. 

-  ^  -  >• 


14.  See  §360. 


[Elements  of  Natural  Philosophy,  pp.  255-260.]  149 

§373.  See  Frick's  "Physical  Technics,"  p.  315 
(§§  277-279). 

§  382.  To  show  that  the  R  M.  F.  of  a  cell  does  not 
depend  upon  the  size  of  the  plates,  connect  two  similar 
cells  in  opposition  (i.  e.,  connect  the  two  -f  plates  to  each 
other  and  the  two  —  plates  to  each  other),  with  a  galva- 
nometer in  the  circuit,  and  notice  the  deflection  (=  0). 
Lift  one  of  the  zincs  nearly  out  of  the  liquid.  The  deflec- 
tion  is  still  zero.  Neither  cell  has  an  excess  of  E.  M.  F. 
We  increased  the  internal  resistance  in  the  cell  operated 
upon,  but  this  affected  the  resistance  of  the  whole  circuit 
ill  which  both  cells  are.  They  are  equally  affected  by  the 
increased  resistance.  If  two  cells  of  different  kinds  be 
thus  joined,  the  galvanometer  needle  will,  in  all  proba- 
bility, show  a  deflection,  owing  to  a  difference  in  the 
E.  M.  F.  of  the  opposing  cells. 

§  383.  Using  a  copper  and  amalgamated  zinc  battery  (see  Fig.  179 
of  text-book)  or  the  bichromate  battery  (see  Fig.  183),  place  a  galva- 
nometer (§  418)  in  the  circuit  and  notice  the  deflection.  Slowly 
raise  one  or  both  of  the  plates  out  of  the  liquid,  noticing  the  decreas- 
ing deflections  of  the  needle.  The  diminution  of  current  is  due  to 
the  increased  internal  resistance,  for  we  have  reduced  the  transverse 
section  of  our  liquid  prism. 

Next,  place  the  strips  in  the  liquid  (Fig.  179)  and  notice  the  de* 
flection  as  before.  Moving  the  strips  further  from  each  other,  the 
deflection  again  falls.  We  have  now  weakened  the  current  by  in- 
creasing the  internal  resistance  by  lengthening  our  liquid  prism. 
See  §883. 

None  of  these  changes  affects  the  E.  M.  F.  of  the  cell  used. 


150  [Elements  of  Natural  Philosophy] 


Exercises,  Page  264. 

12 

2.  See  §  386.    ^t-t  =  1.  Ans.,  1  ampere, 

3-    2oho  =  °X 

4.  Its  diameter  is  4  times  as  great ;  its  sectional  area 
(and,  hence,  its  conductivity  per  linear  unit)  is  16  times 
as  great ;  its  resistance  per  linear  unit  is  only  -^  as  great ; 
it  may,  therefore,  be  made  16  times  as  long, 

12  yd.  x  16  =  192  yd. 
o 

5.  See  §  386.  =  0.2.  Ans.,  0.2  amperes. 

6-  loh  =  °-133- 

Ans.,  0.133  amperes  or  133  milliamperes. 

7.  1  ohm  x    ^)  X  w  =  0.34. 

J?  TP 

8.  G  =  -o-;  2  =  — ;   ^  =  18.  -4ws.,  18  volts. 

9.  C  =  -5- ;  1  =  » ;  R  =  10.     The  total  resistance  is 

10  ohms.     This,  less  the  external  resistance  (5  ohms),  gives 
the  internal  resistance.  Ans.,  5  ohms. 

10.  flr=f;l*=J;*  =  ^5  =  8«. 

§  388.  For  methods  of  cleaning  mercury,  see  Pickering's 
"  Physical  Manipulation,"  p.  35. 


[Elements  of  Natural  Philosophy,  pp.  266-270.]         151 

§  389.  Connect,  in  opposition,  two  cells — one  that  bus 
been  working  for  ten  minutes  and  one  that  is  fresh.  The 
deflection  of  a  galvanometer  in  the  circuit  will  show  that 
the  fresh  cell  has  the  greater  E.  M.  F. 

§  390.  Concerning  the  construction  and  maintenance 
of  very  many  forms  of  battery,  see  M  Scientific  American 
Supplements,"  Nos.  157,  158  and  159.  Price,  10  cents 
each. 

§  392.  This  is  often  called  the  Grenet  battery  or  cell.  A 
teaspoonful  or  two  of  mercury  disulphate  placed  in  the 
solution  will  aid  in  keeping  the  zinc  well  amalgamated. 

Trouve's  solution  is  said  to  be  more  nearly  free  from  the 
troublesome  formation  of  crystals.  The  recipe  is  as 
follows : 

3  ounces  of  potassium  dichromate. 

9     "  sulphuric  acid. 

1  pint  of  water. 

§  393.  These  cells  are  now  sold  in  great  numbers.  At 
the  beginning  of  188G,  the  cells,  complete  with  sal-ammo- 
niac, were  sold  at  85  cents  each.  Directions  accompany 
each  cell.  There  is  little  danger  of  its  freezing.  The  in- 
ternal resistance  of  a  cell  is  said  to  be  about  1  ohm. 

§394.  The  internal  resistance  of  this  battery  (of  con- 
stant E.  M.  F.)  is  very  variable,  ranging,  it  is  said,  from  3 
to  5  ohms.  Never  use  a  cracked  porous  cup  in  this  or  any 
other  battery.  The  plates  and  cups  require  cleaning  after 
about  two  months'  use. 

§  395.  This  is  not  well  adapted  for  school  laboratory 
use,  as  the  liquids  are  likely  to  become  mixed  when  the  cell 
is  moved.  The  wire  leading  up  through  the  liquid  from 
the  copper  plate  should  be  kept  carefully  insulated.  A 
break  in  the  insulation  may  be  repaired  with  asphalium 
paint  or  shellac  varnish.  The  internal  resistance  is  from  2 
to  4  ohms.     Th«  parts  above  the  liquid  should  be  dipped 


152  [Elements  of  Natural  Philosophy,  pp.  210-272.] 

in  melted  paraffine  wax.  A  few  drops  of  oil  on  the  liquid 
will  check  evaporation, 

§  397.  The  potassium  di-chromate  solution  mentioned  in 
§  392  may  be  used  instead  of  the  nitric  acid.  The  offen- 
sive fumes  are  not  so  abundant.  The  porous  cups  of 
Bunsen  or  Grove  cells  should  be  kept  in  water  when  not 
in  use  to  prevent  their  being  cracked  by  the  crystallization 
of  zinc  sulphate  within  their  pores.  After  the  battery 
has  been  used,  it  is  well  to  rinse  the  zincs  and  carbons, 
first  in  water  and  then  in  dilute  hydrochloric  acid  and  then 
to  soak  the  carbons  in  water  for  a  day  or  two.  Carefully 
avoid  spilling  any  of  the  contents  of  the  porous  cup  into 
the  outer  vessel. 

§  398.  See  Frick's  "Physical  Technics,"  p.  319  (§  280). 

To  show  the  importance  of  good  connections,  put  a  galvanometer 
into  the  circuit.  Use,  for  some  of  the  connections,  one  or  more  wires 
that  have  become  rusty  or  corroded  by  exposure  to  acid  fumes. 
Notice  the  deflection.  Then  clean  all  of  the  rusty  connections  by 
scraping  them  with  a  knife  (no  practical  electrician  can  keep  his 
knife  well  sharpened)  and  again  send  the  current  through  the  galva- 
nometer, noticing  the  increased  deflection.  Vary  the  experiment  by 
twisting  connecting  wires  together  loosely  and  then  tightly,  noticing 
the  deflection  in  each  case.  Be  careful  not  to  join  cells  in  opposition, 
i.  e.,  so  that  the  current  from  one  or  more  shall  flow  in  a  direction 
opposite  to  that  of  the  others. 

Sometimes  a  battery  seems  unaccountably  weak.  The  fault  may 
be  in  a  single  cell.  To  test  this  and  to  locate  the  faulty  cell  if  there 
be  one,  join  the  cells  in  series  with  a  galvanometer  in  the  circuit. 
Then  throw  cell  after  cell,  in  succession,  out  of  the  circuit  (by  re- 
moving or  short  circuiting  it),  noticing  the  deflection  of  the  galva- 
nometer as  the  current  is  shunted  by  each  successive  cell.  At  each 
trial,  after  the  first,  all  of  the  cells  but  one  are  in  the  circuit.  If  the 
sucessive  deflections  do  not  vary  much,  the  cells  are,  probably,  in 
equally  good  condition.  If,  however,  the  dropping  of  any  cell  pro- 
duces a  marked  variation  in  the  deflection,  that  cell  is  faulty. 

The  several  cells  of  the  battery  should  not  touch  each  other,  and 
their  supports  should  be  kept  dry.  Each  cell  may  well  stand  on  three 
small  porcelain  knobs.  They  should  be  connected  by  stout  copper 
wires,  well  insulated.  Paraffine  insulation  is  desirable  as  it  well 
resists  the  action  of  the  acids  and  acid  fumes. 


[Elements  of  Natural  Philosophy,  p.  e?4.]  153 

§  402.  This  does  not  mean  that  the  external  or  the  in- 
ternal resistance  is  to  be  increased  for  the  sake  of  pro- 
ducing an  equality,  but  that  t he  cells  shall  be  grouped  so 
as  to  make  the  internal  resistance  as  nearly  equal  as  possi- 
ble to  the  necessary  external  resistance,  which  will  be 
determined  by  the  circumstances  of  the  case.  Ohm's  law 
shows  that  the  internal  resistance  is  a  positive  disadvantage, 
but  it  is  an  unavoidable  accompaniment  of  high  E.  M.  F. 
Representing  the  internal  resistance  of  a  single  cell  by  r 
and  the  total  external  resistance  by  R,  and  the  number  of 
cells  in  the  battery  by  n,  the  maximum  current  strength 
will  be  secured  when  the  number  of  cells  joined  abreast 

equals  y  -^  .     For  example,  if  we  have  40  cells,  each  with 

an  internal  resistance  of  3  ohms,  to  be  worked  with  an. 
external  resistance  of  8  ohms,  we  see,  by  this  formula, 

/40  x  3 
that  the  number  joined  abreast  should  be  y  - —  =  4 

o 

(nearly).  Each  group  of  4  cells  should  be  joined  in  mul- 
tiple arc  and  the  ten  groups  joined  in  series. 

Gordon's  rule  is  as  follows  :  To  obtain  a  maximum 
current,  the  ratio  of  the  number  of  cells  in  series  to  the 
number  of  cells  joined  abreast  should  equal  the  ratio  of 
the  external  resistance  to  the  resistance  of  a  single  cell. 

Representing  the  number  of  cells  joined  tandem  by  JV 
and  the  number  of   cells  joined  abreast  by  n,  this  gives 

*l  -  a 

n  '  '   r 

In  the  case  given  above,  the  number  of  cells,  40,  must 

be  divided  into  two  such  integral  factors  that  one  divided 

R         8 
by  the  other  shall,  as  nearly  as  possible,  equal  —  or  ■=. 

The  best  that  can  be  done  is  to  divide  the  cells  into  10 

groups  of  4  each. 

N       R        10        8  . 

—  =  —  or  -r-  as  5  nearly. 
n        r  4         3  J 


154  [Elements  of  Natural  Philosophy. .] 


Exercises,  Page  275, 

1-°  =  §  =  m>i  =  1-9996+- 


2.  Internal  resistance  (      )  is  0.5  ohm. 
1 


(fj«- 


0.501 

3-  «j£i>I  =  0-199"  + 

4-  tt^f  =  0.00099502. 
1005 

5-  IO0V5  *  a000"95- 
0.00952. 


=  1.996  +  , 


1050 

7.  Because  the  line  and  the  instruments  offer  a  high 
resistance  and,  under  such  circumstances,  this  arrange- 
ment results  in  the  greatest  current  strength. 

9.  The  resistance  of  No.  6  wire  is  found  (from  the 
table)  to  be  0.411  ohms  per  1000  feet,  or  2.17  ohms  per 
mile.  The  total  line  resistance  is,  therefore,  21.7  ohms. 
This  is  4.8  times  the  resistance  of  a  single  lamp.  As  the 
fractional  part  of  a  lamp  can  not  be  cut  out,  it  is  neces- 
sary to  remove  or  short  circuit  5  lamps. 

10.  See  Fig.  190  or  Fig.  206,  omitting  the  galvanometer 
from  the  latter  or  considering  it  one  of  very  small  re- 
sistance. 

12.  In  App.  K  (2),  the  specific  resistance  of  pure  water 

is   more   than    50   times   that   of    dilute   sulphuric   acid 

7  18 
(•|  water  and  £  acid).    ^-— >  =  57.     Then  the  conductivity 

of  the  dilute  acid  is  more  than  50  times  that  of  water. 

7  18 

13.  See  App.  K  (2).    ^— °-  =  22,  nearly. 


[Elements  of  Natural  Philosophy,  pp.  278-383.]  155 

§  404  (c).  For  example,  suppose  that  the  three  wires 
placed  abreast  haVe  separate  resistances  of  a,  b  and  c  ohms 
respectively.     Then   their  several   conductivities   will   be 

represented  by  -,  ^  and  -  and  their  joint  conductivity  by 

1       1       1       ab  +  ac  +  be        ...      .  .   .        .  ,  ... 

-  +  T  +  -  = ■ — r— - — ,  and  the  joint  resistance  will 

a      be  abc  * 

be  -r — j- .     Now,  suppose  a  particular  case  in  which 

a,  b  and  c  represent  3,  4  and  5  ohms  respectively.  We 
easily  write  out  the  result  at  once  : 

12  +  15  +  20  =  47  =  1H'  thG  immber  °f  0hm8* 

§  406.  See  Frick's  "Physical  Technics,"  p.  336  (§§  292, 
293).    . 

§  408.  See  Frick's  "  Physical  Technics,"  p.  311  (§  275) 
and  p.  334  (§§  290,  291). 

Experiment  76.  — 
The  acompanying  fig- 
ure better  shows  the 
arrangement  of  the 
apparatus. 

§410.  Solder  a  pla- 
tinum strip  2  cm.  by 
5  cm.  to  each  of  two 
stout  copper  wires  20   \ 
cm.   long.      Pass  the    ^^^HBB 
wires  through  the  neck 

of  a  glass  funnel.  Thrust  a  cork  into  the  lower  end  (  f 
tin'  funnel  neck,  seeing  that  the  wires  are  on  opposite  sides 
of  the  cork.  Warm  the  funnel  carefully  hut  considerably, 
place  it  upright  and  poor  into  it  melted  sealing-wax  until 
the  wax  covers  the  lower  ends  of  the  platinum  Btripa 
When  the  wax  is  cool,  it  constitutes  a  [rood  floor  for  the 
Support  of  the  inverted  test-tubes  as  shown   in    Fig.  194. 


156  [Elements  of  Natural  Philosophy,  pp.  283-286.] 

A  retort  stand  (see  Fig.  301)  furnishes  a  convenient  sup- 
port for  the  funnel.  Of  course,  the  binding  posts  shown 
in  Fig.  194  are  in  no  wise  important.  The  funnel  may 
be  provided  with  a  tin  or  paste- board  cover  through  which 
the  test-tubes  pass  and  by  which  they  may  be  held 
upright.     See  "  Nature/'  Vol.  35,  p.  131. 

See  Frick's  "Physical  Technics,"  p.  340  (§§295-29?) 
and  Deschanel's  "  Natural  Philosophy,"  §  600. 

To  a  solution  of  salt,  add  a  few  drops  of  a  solution  of  potassium 
ferro-cyanide,  better  known  as  yellow  prussiate  of  potash.  With 
this,  wet  a  sheet  of  white  paper  and  lay  the  paper  on  a  sheet  of  tin. 
Connect  the  tin  with  the  wire  from  the  negative  pole  of  a  gal- 
vanic battery.  See  that  the  wire  from  the  other  pole  terminates 
in  an  iron  wire  or  stylus  and,  with  it,  write  upon  the  paper.  The 
current  passes  through  the  moistened  paper,  leaving  a  blue  trace 
thereon. 

Vary  the  above  experiment  by  using  a  solution  of  potassium 
iodide  and  starch  with  which  to  moisten  the  paper.  Prepare  the 
solution  by  boiling  30  cu.  cm.  of  water  and  stirring  into  it  0.5  g.  of 
starch  previously  reduced  to  the  consistency  of  cream  by  thoroughly 
mixing  it  with  a  few  drops  of  water.  In  this,  dissolve  a  piece  of 
potassium  iodide,  half  the  size  of  a  pea.  See  Elem.  Chemistry, 
Exp.  100.       • 

"  We  have  reason  to  believe  that  water  is  not  an  electrolyte  and 
that  it  is  not  a  conductor  of  the  electric  current.  It  is  exceedingly 
difficult  to  obtain  water  free  from  foreign  matter.  Kohlrausch, 
however,  has  obtained  water  so  pure  that  its  resistance  was  enor- 
mous compared  with  ordinary  distilled  water.  When  exposed  to 
the  air  for  4.3  hours,  its  conductivity  rose  70  per  cent,  and  in  1060 
hours  it  was  increased  nearly  forty  fold.  The  oxygen  and  hydrogen 
which  are  given  off  at  the  electrodes  in  so  many  experiments  en 
water  containing  foreign  ingredients  are,  therefore,  not  the  ions  of 
water  separated  by  strict  electrolysis,  but  secondary  products  of  the 
electrolysis  of  the  matter  in  solution." — Maxwell. 

%  412.  A  silver  salt  solution  may  be  prepared  as  follows  :  Place  a 
silver  coin  in  a  large  test  tube  and  add  a  little  of  nitric  acid  (HN03). 
Warm  the  tube  and  contents  to  hasten  the  chemical  action.  The 
coin  will  dissolve  with  the  evolution  of  reddish  fumes  due  to  the 
presence  of  the  copper  alloy  of  the  coin.     The  liquid  now  contains 


[Elements  of  Natural  Philosophy,  p.  ?S>;.]  157 

solutions  of  silver  nitrate  (AgNO,)  and  copper  nitrate,  the  green  color 
being  due  to  the  latter.  The  copper  nitrate  is  not  of  any  use  to  us 
in  this  experiment  ;  we  have  it  because  it  is  more  difficult  to  get  pure 
silver,  than  it  is  to  get  rid  of  the  copper  nitrate.  Nearly  fill  the 
tube  with  pure,  soft  water.  Add  hydrochloric  (muriatic)  acid  (HCI), 
or  a  strong  aqueous  solution  of  common  salt  (NaCI)  drop  by  drop. 
The  chlorine  (CI)  of  the  acid  or  of  the  salt  will  combine  with  the 
silver  (Ag)  of  the  silver  nitrate  and  form  silver  chloride  (AgCI).  The 
silver  chloride  thus  formed  will  fall  to  the  bottom  of  the  test-tube 
as  a  solid,  white  precipitate.  When  so  much  of  the  acid  or  brine 
has  been  added  that  silver  chloride  is  no  longer  precipitated,  care- 
fully pour  the  colored  liquid  from  the  test-tube  ;  add  pure,  soft 
water,  shake  thoroughly,  let  the  precipitate  settle  and  pour  off  the 
liquid  as  before.  In  this  way,  wash  the  silver  chloride  several 
times.  Dissolve  a  little  of  potassium  cyanide  in  warm  water 
(N.B. — Potassium  cyanide  is  intensely  poisonous,  not  only  when  taken 
internally,  but  even  when  brought  into  contact  with  an  abrasion  of  the 
skin,  a  cut  or  scratch.)  Pour  this  solution  in  small  quantities  into 
the  test-tube  until  the  silver  chloride  is  nearly  dissolved.  It  is  well 
to  add  the  solution  of  potassium  cyanide  drop  by  drop,  so  that  there 
be  no  excess  of  it.     The  solution  is  now  ready  for  the  bath. 

It  will  interest  the  pupils  to  have  each  of  them  construct 
a  battery  and  perform  the  work  of  electrotyping. 

Fasten  a  wire  to  a  coin  (or  other  small  conductor  of  electricity), 
coat  the  wire  with  wax  or  varnish,  place  the  coin  in  a  bowl  and  half 
fill  the  bowl  with  a  saturated  solution  of  copper  sulphate  (blue 
vitriol).  Tie  a  piece  of  bladder  over  the  larger  end  of  a  lamp 
chimney  and  place  the  porous  cup  thus  made  in  the  bowl,  support- 
ing it  so  that  the  bladder  will  be  a  little  ways  above  the  coin.  In 
the  porou  cup,  place  some  very  dilute  sulphuric  acid.  In  the  acid, 
sii-j.cikI  by  ■  wire  a  roll  of  sheet  zinc  previously  amalgamated 
)  Join  the  wires  from  the  zinc  and  the  coin.  (See  §  394,  a.) 
When  th.  mins  copper  coat  has  become  thick  enough,  it  may  be 
•tripped  off  as  a  reversed  copy.  This  reversed  copy  may  now  be  sub- 
set ut.'<l  for  the  coin,  as  the  negative  electrode,  and  a  direct  copy  of  the 
coin  thus  produc.,1. 

See  Prick's  "  Physical  Technics,"  p.  343  (§§  298-301) 

Natural  Philosophy,"  §  606. 


158  [Elements  of  Natural  Philosophy,  pp.  290-297.] 

§  416.  "If  the  rod  be  of  considerable  size,  say  a  footoi 
more  in  length  and  half  an  inch  or  more  in  diameter,  and 
the  current  be  strong  enough  to  make  a  powerful  magnet 
of  it,  whenever  the  current  from  the  battery  is  broken,  the 
bar  may  be  heard  to  give  out  a  siugle  click.  This  will 
happen  as  often  as  the  current  is  broken.  This  is  occa- 
sioned by  a  molecular  movement  which  results  in  a  change 
of  length  of  the  bar.  When  it  is  made  a  magnet  it  elon- 
gates about  -g-gimr  °^  ^s  length  ;  and  this  change  is  accom- 
panied with  the  sound." — Dolbear. 

§  417.  The  following  device  of  Ampere's  may  aid  the 
memory :  Suppose  a  man  to  be  placed  in  the  circuit  so  as 
to  face  the  needle  and  so  that  the  current  shall  enter  at 
his  feet  and  leave  at  his  head.  The  —  pole  will  turn  to- 
ward his  left.  See  Frick's  "  Physical  Technics,"  pp.  368^ 
386,  Deschanel's  "  Natural  Philosophy,"  §§  531,  548,  and 
Jenkin's  "  Electricity  and  Magnetism,"  chap.  xiii. 

§  418.  See  Frick's  "Physical  Technics,"  p.  351  (§  304). 

Exercises,  Page  296. 

3.  The  pupils  should  be  encouraged  to  give  something 
other  than  Experiments  73-75. 

4.  See  §§  418  and  505. 

5.  (a.)  3.58  ohms  x  4.4  =  15.752  ohms. 

(b.)  1  ohm  requires  20  yd.     13.2  ohms  requires  13.2 
times  20  yd.  =  264  yd.     Or, 

5:  13.2::  100:  264.      Or,  ^  =  f^. 

5  100 

6.  8.29  ohms  x  (££)2  =  12.56  ohms. 

7.  0.91  ohm  x  *fff-  =  1.72  ohms. 

8.  (c.)  By  the  electrolysis  of  some  soluble,  chemical 
compound  of  the  substance. 

9.  1.3  ohms  :  4.55  ohms  =  1  mile  :  3.5  miles. 

10.  23  ohms  :  10.82  ohms  =  (70)2 :  (48)2. 


[foments  of  Natural  Philoxophy.  pp.  297,  S9$.]         159 

11.  The  silver  wire  (being  *f  the  same  size)  may  1  ■• 
many  times  longer  as  its  conduetivity  is  times  greater. 

10  inches  x  1.04G7  as  10.4G7  inches.— Ans. 

12.  An  eqoft]  length  of  the  second  wire  would  weigh  20 
grams  and  have  a  resistance  of  37  ohms.     See  §  379  (2). 

20 
37  ohms  x   jrx-=  =  14.1  ohms.     Or, 

52.5  g  :  20  g  =  37  ohms  :  14.1  ohms. 

E 

13.  C=-~.     When  the  wire  was  removed,  the  resist- 

K 

ance  was  lessened,  the  E.  M.  F.  remaining  the  same.    This 
led  to  an  increased  strength  of  current. 

14.  There  are  1700  yd.  in  a  mile. 

1  ohm  x  tWjt  x  (£H)2  =  °-55  onm- 

15.  10.09  ohms  :  1.15  ohms  =  95* :  322. 

1G.  When  the  external  part  of  the  circuit  is  of  small 
resistance.     §402  (E). 

hr)    = 


/  i  \2  _ 

X   \0.74j    - 


18.  See  §  402,  (a)  and  (d). 

19.  1000  yd.  x  4  x  \  =  571*  yd- 

20.  See  §  404  (c).     gAJ?  =  16.87. 

21.  1  :  7  =  (2.5)2  :  (6.61)2. 

20 

22.  See  §  411(a).  -g^jj^  =  58,607.7,  the  number  of 

coulombs. 

S3.  This  requires  95,050  coulombs.  §  410  (c).  Each 
coulomb  requires  0.00084185  g.  of  zinc  in  each  cell  tbrongfa 
which  it  passes.  §411  (a).  The  necessary  number  of 
coulombs  will  require  0.00034125  g.  x  95,050  =a  32.5  g. 
<  Dearly). 

24.  *See§411  (b).  0.0003307  g.  X  95,050  =  31.5  g. 
(nearly). 


1 60  [Elements  of  Natural  Philosophy,  pp.  298,  299.] 

26.  G  =  f      .-.   10 


R  4.5  x  60  +  10  +  22 

.-.   E  =  3,020  volts. 

27.  The  copper  and  zinc  constitute  the  two  plates  of  a 
voltaic  battery  when  placed  in  the  acid  solution.  As  they 
are  in  contact,  the  current  is  closed  through  the  two 
metals  and  the  liquid.  The  current  in  traversing  the 
liquid,  electrolyzes  it  and  deposits  the  electro-positive 
lead  upon  the  copper  (or  negative)  electrode. 

28.  The  current  will  be  the  stronger  at  20°  0. 

29.  10  inches  x  0.0923  =  0.923  inch.—  Ans. 
30.— 

5.5x18x3.7x2.9 

5.5  x  3.7  x  2.9  +  5.5  x  18  x  2.9  +  5.5  x  18  x  3.7  +  18  x  3.7  x  2.9 
=  1.17. 

81.  Let  x  ==  the  number  of  lamps. 

Then  the  total  current  in  the  external  circuit  =  1.6  as. 

§  386.  R  =  ~      .-.  Total  resistance  =  ^- . 

55 

External  resistance  =  -— ; 0.032  ohms. 

1.6x 

28 
External  resistance   also  =  —  ohms. 

x 

Equating  these  values, 

^  =  J^_  0.032. 
x         l.Oas 

.-.     x  =  199. 

§  424.  See  Frick's  "Physical  Technics,"  p.  241  (§  213- 
217). 


[Elements  of  Natural  Philosophy,  pp.  SO  IS  15.]  161 

§  429.  "  Dip  similar  poles  of  two  magnets  into  iron  filings  and 
bring  them  close  together;  the  projecting  filings  will  repel  each 
other.  Repeat  the  experiment  with  unlike  poles;  the  filaments  will 
interlock  like  the  arms  of  a  polyp  around  its  prey." 

§  431.  For  a  view  of  apparatus  for  diamagnetism,  sec 
Deschauers  ''Natural  Philosophy,"  Fig.  432. 

.    §  433.  See  Daniell's  "Principles  of  Physics,"  pp.  184, 
185. 

§  436.  By  a  brass  or  copper  wire,  suspend  a  red-hot  iron 
ball  near  the  pole  of  a  powerful  electro-magnet.  The  ball 
will  not  be  attracted  until  it  has  cooled  considerably.  This 
shows  that  when  the  iron  molecules  are  agitated  (§  538)  to 
a  red- heat,  the  iron  mass  can  not  be  magnetized.  See 
§454. 

§  437.  See  Frick's  "  Physical  Technics,"  p.  251  (§  228). 

§  440.  If  by  an  untwisted  thread  and  a  wire  stirrup  we 
support  an  unmagnetized  needle  mounted  upon  an  axis 
passing  through  the  needle's  centre  of  gravity  (Fig.  222), 
the  needle  will  remain  in  equilibrium  whatever  its  posi- 
tion. (§  113.)  Magnetize  now  the  needle;  it  will  be  no 
longer  passive,  but  will  place  itself  in  a  particular  vertical 
plane,  and  in  a  particular  position  in  that  plane.  The 
vertical  plane  will  be  nearly  north  and  south  (§  441):  the 
needle's  position  in  the  plane  will  not  be  horizontal,  ex- 
cepting at  the  magnetic  equator. 

§  441.  As  the  Line  of  no  Variation  is  moving  westward, 
the  variation  at  any  given  place  is  continually  changing. 
These  changes  in  variation  are  of  more  practical  impor- 
tance than  the  amount  of  variation.  Hence  the  date  of  a 
survey  is  important.  Without  the  date  and  proper  allow- 
ance for  change  in  variation,  it  would  be  impossible 
correctly  to  resurvey  a  farm  by  the  "bearings"  recorded 
in  an  old  deed.  Hence  much  litigation.  See  Harper's 
MagaaiM  for  March,  1879,  pp.  510,  512,  520. 


102  [Elements  of  Natural  Philosophy,  pp.  315-325.] 

In  1880,  the  westerly  declination  in  degrees  at  Halifax 
was  20.3;  at  Cambridge,  Mass.,  11.63  ;  at  New  York  City, 
7.84;  at  Washington,  3.26;  at  Erie,  Pa.,  2.31,  while  the 
easterly  declination  at  New  Orleans  was  6.62  ;  at  San 
Francisco,  16.52  ;  at  Sitka,  28.5.  In  1886,  the  declination 
at  Cambridge  was  11.8  westerly. 

Exp.  102.  See  Hand-Book  note  on  §  470. 

§  442.  See  Frick's  "Physical  Technics,"  p.  241  (§  213) 
and  p.  368  (§§  313,  314). 

§  44g.  A  method,  represented  in  the  figure,  is  known 
as  "  the  double  touch."    The  opposite  poles  of  two  mag- 


nets are  kept  at  a  fixed  distance  from  each  other  by  means 
of  a  wooden  block  placed  between  them.  The  magnets, 
thus  held,  are  moved  from  the  middle  toward  one  end  of 
the  bar,  thence  to  the  other  end,  repeating  the  operation 
several  times  and  finishing  at  the  middle  when  each  half 
of  the  bar  has  received  the  same  number  of  frictions.  See 
Frick's  "Physical  Technics,"  p.  247  (§§  220-224). 


[Elements  of  Natural  Philosophy,  pp.  325,  326.] 
§  449.  The  armature  is  sometimes  the   iron  axle  of  a 


brass  wheel,  as  shown  in  the  figure.     It  is  then  called  a 
rolling  armature. 

Hold  a  horseshoe  magnet  by  its  middle,  slightly  depress  the  poles, 
place  the  iron  axle  upon  the  arms  of  the  magnet  and  allow  it  to 
roll  to  the  end.  Its  momentum  will  carry  the  axle  around  the  ends 
of  the  magnet  and  the  wheel  will  roll  back  to  the  middle,  with  the 
axle  on  the  under  side  of  the  magnet. 

§  452.  These  practical  units  are  often  called  British 
Association  units  or  B.  A.  units.  They  may  be  regarded 
as  derived,  not  from  the  centimeter,  gram  and  second 
(C.  G.  S.)  as  fundamental  units  but  from  a  system  where 
the  unit  of  space  is  the  earth -quad  rant  (§  25);  the  unit  of 
mass  is  10~u  gram  and  the  unit  of  time  is  a  second.  See 
Hand-Book  note  on  §  359. 

§  454.  Concerning  the  medium  involved  in  electromag- 
netic phenomena,  see  "  Encyclopaedia  Britannica,"  Vol.  8, 
p.  571  (ninth  edition). 


164 


[Elements  of  Natural  PJiilosophy.'] 


Exercises,  Page  328. 

2.  (b.)  See  §  429  (1). 

3.  See  §  432. 

4.  By  suspending  it  in  a  stirrup  or  otherwise  so  that  it 


may  turn  easily  and  seeing  which  pole  pointed  northward. 
This  will  he  the  —  pole.  Or  it  may  be  tested  by  a  mag- 
net of  known  polarity  as  shown  in  the  accompanying 
figure. 

5.  It  will  lie  in  a  vertical  plane,  extending  nearly  north 
and  south,  with  an  inclination  nearly  equal  to  the  latitude 
of  the  place  (§  440).     See  Fig.  222. 

0.  (c.)  The  magnetic  and  geographical  meridians  coin- 
cide at  all  points  in  the  line  of  no  variation  and  not  else- 
where.    See  §  441. 

7.  It  does  not.  The  attraction  of  the  north  pole  of  the 
earth  for  the  —  pole  of  the  needle  is  counterbalanced  by 


[Elements  of  Natural  Philosophy,  pp.  328,  329.]         165 

its  repulsion  for  the  -f  pole  of  the  needle.  The  accom- 
panying figure  shows    the — 

way  in  which  the  needle  is  i      xa  __©__ 

placed  in  a  north  and  south    \L~:     ~~~  . "       \ 

line.     The  arrow,  a,  repre-     vS        I  -,*db  \ 

sents  the  attraction  of  the      V    \c  \  \ 

north  magnetic  pole  of  the        \  _\ 

earth  and  c  represents  the 

repulsion  of  the  south  magnetic  pole  of  the  earth  acting 
upon  the  —  pole  of  the  needle  ;  b  represents  the  repul- 
sion of  the  north  pole  and  d  represents  the  attraction  of 
the  south  pole  of  the  earth  acting  upon  the  -|-  pole  of  the 
needle.  The  combined  effect  of  these  four  forces  is  to 
place  the  needle  in  the  magnetic  meridian.  When  the 
needle  is  thus  placed,  since  the  two  ends  of  the  needle  are 
practically  equidistant  from  either  pole  of  the  earth, 
a  +  c  ==  b  +  d.  The  two  couples  (see  note  on  §  86,  p.  51 
of  this  volume)  thus  counterbalance  each  other. 

8.  (c.)  S  =  \gf*  =  16.08//.  x  121  b=  1945.68//.— A n& 

9.  They  should  be  made  of  fine  wire.     §  403. 

10.  Use  a  long  coil  galvanometer.     §  403. 

11.  It  would  not.     §  385. 

12.  Four  ohms.  Make  the  external  resistance  equal  to 
the  internal.     §  402  (d.) 

13.  Each  series  of  two  cells  has  an  .internal  resistance 
of  6  ohms.  There  being  3  such  scries,  the  internal  resist- 
ance of  the  battery  (§  400,  a)  is  6  ohms  divided  by  the 
number  of  such  series,  or  2  ohms.  The  external  resist- 
ance should  be  equal  to  this. 

14.  "  The  power  of  an  electro-magnet  depends  largely 
upon  the  number  of  times  a  given  current  circulates 
around  its  core  and  upon  the  nearness  of  the  current  to 
the  core  ;  for  compactness,  and  to  keep  the  current  near 
the  core,  a  fine  wire  must  then  be  used.  But  a  long,  thin 
wire  would  offer  large  resistance  that  might  so  reduce  the 


166         [Elements  of  Natural  Philosophy,  pp.  329,  330.] 

current  as  more  than  to  offset  the  advantage  that  would 
otherwise  be  gained.  Hence,  token  there  is  little  other  re- 
sistance in  a  circuit,  a  large  wire  with  few  turns  will  give 
the  strongest  electro-magnet.  But  if  an  electro-magnet  is 
to  be  used  in  a  circuit  with  other  large  resistance,  then  the 
introduction  of  a  helix  of  many  turns  of  fine  wire  would 
add  little  more  resistance  comparatively,  and  the  strength  of 
the  current  would  be  reduced  but  little,  while  a  great  gain 
would  be  made  in  the  effect  on  the  core." 

15.  See  Appendix  M  [4(a)]. 

216  ohms:  150  ohms  =  10.79  volts  :  7.945  volts. 
The  E.  M.  F.  of  the  Leclanche  battery  is  7.945  volts— 
and  that  of  each  cell  is  \  thereof,  or  1.499  volts. 

E 

16.  C  =  -w  .     The  resistance  of  the  line  is  55.8  ohms. 

•020  =  n,    EKKO     .-.  E  =  1.126  volts. 
0.5  H-  55.8 

As  a  single  cell  has  an  E.  M.  F.  greater  than  that  re- 
quired by  the  conditions,  one  cell  will  answer. 

17.  No.  The  E.  M.  F.  being  1.079  volts  and  the  resist- 
ance of  the  circuit  being  1432  ohms,  the  current  yielded 
will  be  less  than  1  milliampere;  not  nearly  enough  to 
work  the  instrument. 

18.  Under  no  circumstances. 

19.  First,  in  their  origin.  Electric  charges  may  be 
developed  in  a  very  great  variety  of  substances  ;  very  few 
substances  can  be  magnetized.  Second,  in  the  nature 
of  the  bodies  acted  on.  Electric  charges  act  on  bodies 
of  all  substances ;  very  few  substances  are  magnetic. 
Third,  they  differ  in  that  every  magnet  has  two  poles 
having  opposite  properties,  whereas  an  electrified  body 
may  have  similar  properties  in  every  part  of  its  surface. 

20.  The  voltaic  cell  has  become  polarized.     §  389. 

21.  The  problem  is  indeterminate  as  stated.  If  the  re- 
sistances (10  and  100  ohms)  are  unplugged,  as  shown  in 


[Memento  of  Natural  Philosophy,  p.  330.]  16? 

A  and  C  of  Fig.  407,  and  the  unplugged  resistances  of  B 
are  281  ohms,  we  have  the  proportion, 

10  :  100  =  281  :  2810.     Ans.,  2810  ohms. 

But  if  the  resistance  of  100  ohms  is  in  A  and  that  of  10 
is  in  B,  we  have 

100  :  10  ::  281  :  28.1.     Ans.,  28.1  ohms. 

1  -.'.  Relays  are  placed  in  the  main  circuit  which  is  of 
high  resistance.  Sounders  are  placed  in  the  local  circuit 
which  is  of  low  resistance.    §  403. 


168  \Ekinent8  of  Natural  Philosophy,  pp.  332-341.] 

§  456.  See  Frick's  "  Physical  Technics,"  p.  386.  This 
is  a  very  valuable  book  and  the  teacher  should  own  or 
have  easy  access  to  a  copy  thereof.  The  teacher  will  find 
interest  and  profit  in  reading  Gladstone's  "  Michael  Fara- 
day," published  by  Harper  and  Brothers;  90  cents. 

§  458.  See  Frick's  "Physical  Technics,"  p.  389  (§  326). 
Repeat  Exp.  15,  placing  an  electro-magnet  in  the  circuit ; 
notice  the  increased  brilliancy  of  the  sparks. 

§  460.  Connect  the  terminals  of  the  secondary  coil  to  the  two 
coats  of  a  large,  insulated  Leyden  jar.  Hold  one  ball  of  a  discharger 
(§  355)  on  the  outer  coat  and  the  other  hall  near  the  knob  of  the  jar. 
As  the  jar  has  to  be  charged  between  each  two  successive  sparks,  the 
discharges  will  be  less  frequent  than  those  of  the  coil  alone,  but 
foey  will  be  much  louder  and  more  brilliant. 

§  461.  See  Frick's  "  Physical  Technics,"  p.  387  (§§  324, 
325). 

§  465.  In  the  voltaic  battery,  the  energy  of  chemical  action  is 
eonverted  into  electric  energy  ;  in  the  dynamo  electric  machine,  the 
energy  of  mechanical  action  is  converted  into  electric  energy.  The 
Brush  dynamo  has  like  poles  of  its  two  powerful  horse-shoe  magnets, 
MM,  facing  each  other  on  opposite  sides  of  the  wheel  or  ring  arma- 
ture, R,  as  shown  at  nn  and  8  8  in  the  following  figure.  In  other 
words,  the  two  +  poles  of  the  magnets  are  at  one  extremity  and  the 
two  —  poles  at  the  other  extremity  of  the  same  diameter  of  the 
armature.  Upon  the  commutator,  c,  rest  the  commutator  brushes, 
i  i,  made  of  comb-like  strips  of  copper.  These  brushes  communicate 
indirectly  with  the  two  binding  posts  shown  at  the  right-hand 
end  of  the  base  of  the  machine.  These  posts  represent  the  +  and 
—  poles  of  the  dynamo,  whence,  by  means  of  wires,  the  electricity 
may  be  conducted  to  any  desired  place. 

In  studying  the  action  of  this  machine,  it  will  be  convenient  to 
consider,  at  first,  only  one  pair  of  helices.  As  already  stated,  helices 
on  opposite  sides  of  the  ring  armature  are  connected  in  pairs.  Each 
couple  of  helices  has  its  ring  upon  the  commutator.  In  these  two 
opposite  helices,  a  and  b,  the  currents  are  generated.  As  a  ap- 
proaches the  +  poles  of  the  magnets,  a  current  is  generated  in  that 
helix.  As  b  is,  at  the  same  time,  approaching  the  —  poles,  a  similar 
current  flowing  in  the  opposite  direction  is  generated  in  that  helix. 


[Elements  of  Natural  Philosophy,  p.  S41.] 


169 


The  helices,  a  and  b,  are  so  connrcted  that  these  two  similar  and 
simultaneous  currents  flow  in  the  same  direction  on  the  wire.  A 
moment  later,  when  a  and  b  are  passing  the  "  neutral  point  "  in  the 
magnetic  field,  this  pair  is,  by  the  action  of  the  commutator,  thrown 
out  of  the  circuit  and  another  i»air  thrown  into  the  circuit.  Thus 
the  commutator  secures  a  continuous  flow  of  electricity  in  one  direc- 
tion instead  of  the  interrupted  "to  and  fro"  current  of  the  Ruhm- 
korff  coil.  The  commutator  consists  of  segments  of  brass,  secured 
to  a  ring  of  insulating  material,  carried  on  the  shaft.  These  seg- 
ments are  divided  into  two  thicknesses,  the  inner  being  permanently 
secured  to  the  non-conducting  material,  and  the  outer  ones,  which 


SR 


take  all  the  wear,  are  fastened  to  the  inner  in  such  a  manner  that 
they  can  be  easily  replaced  when  necessary.  In  the  left  hand  figure 
above,  only  two  of  the  helices  are  represented  as  being  connected 
with  each  other  and  with  the  commutator.  In  the  other  figure,  the 
eight  helices  are  represented  as  being  connected.  In  order  to  place 
the  commutator  in  a  convenient  position,  the  terminal  wires  of  the 
helices  are  carried  through  the  centre  of  the  shaft  to  a  point  outside 
the  bearings  and  there  connected  with  the  proper  segments  of  the 
■on  1  mutator.  These  segments  are  so  arranged  that,  at  any  instant, 
three  or  more  pairs  of  helices  are  interposed  in  the  circuit  of  the 
machine,  working,  as  it  were,  in  multiple  arc,  the  remaining  pair 
being  cut  out  at  the  *'  neutral  point." 

The  four  coils  of  the  two  electromagnets  are  placed  in  the  circuit 
between  the  commutator  and  one  of  the  binding  posts,  so  that  the 
whole  of  the  current  generated  by  the  machine  may  be  used  in  exciting 
tjhe  magnet*.  The  iron  of  the  magnets  and  armature,  after  the  first 
operation  of  the  machine,  |  assesses  a  slight  residual  magnetism 
[£  443,  («)J  which  generates  a  feeble  electric  current.     This  current 


170  [Elements  of  Natural  Philosophy,  pp.  34 1-346. ~\ 

increases  the  intensity  of  the  magnets  and  the  excited  magnets,  in 
turn,  intensify  the  currents  in  the  helices.  As  the  machine  is 
worked,  the  magnetism  and  the  electricity  strengthen  one  another 
in  succession  until  the  maximum  effect  of  the  machine  is  reached. 
It  is  found  that  the  iron  of  the  electro- magnets  becomes  sufficiently 
magnetized,  in  the  processes  of  manufacture,  to  start  the  action  of 
the  machine  at  even  the  first  trial  without  further  magnetization 
by  any  external  agency. 

The  advantage  of  winding  the  wire  in  grooves  on  the  armature  is 
twofold.  In  the  first  place,  the  parts  of  the  armature  not  covered 
by  the  helices  may  be  made  to  revolve  much  nearer  the  poles  of  the 
magnets  than  could  be  done  if  the  armature  were  not  grooved  or 
than  would  be  possible  if  it  were  wholly  covered  with  helices  as  in 
the  Gramme  machine.  By  this  increased  nearness  between  the 
armature  and  the  poles  of  the  magnets,  the  inductive  effect  of  the 
latter  is  greatly  increased.  In  the  second  place,  as  the  greater  part 
of  the  armature  is  exposed  to  the  atmosphere,  "  the  heat  which  is 
always  developed  by  the  rapidly  succeeding  magnetizations  and  de- 
magnetizations of  armatures  in  motion  is  rapidly  dissipated  by  radia- 
tion and  convection."  Another  marked  difference  between  this  and 
other  dynamo-electric  machines  "lies  in  the  manner  of  connecting 
the  armature  coils  to  the  commutator,  this  being  such  that  only  the 
particular  coils  which  contribute  to  the  production  of  the  current  are 
in  the  circuit  at  once.  During  the  time  they  are  passing  through  the 
'  neutral  points '  in  the  magnetic  field,  they  are  cut  out  one  after  the 
other,  and  thus,  while  idle,  do  not  tend  to  weaken  the  effects  of  the 
machine  by  affording  a  path  to  divert  the  current  generated  in  the 
active  sections  from  its  proper  channel." 

§  466.  When  the  energy  expended  in  a  lamp  is  increased, 
the  luminous  rays  gain  at  the  expense  of  the  thermal  rays, 
which  are  of  greater  wave  length  (§  716),  so  that  the 
light  emitted  varies  not  as  the  energy  expended,  hut  as 
the  third  power  of  such  energy. 

§  467.  For  description  of  Duboscq's  and  Foucault's  arc 
light  regulators  (now  antiquated  but  of  great  historical 
interest),  see  Deschanel's  "  Natural  Philosophy,"  §§  577, 
578. 

The  intense  heat  developed  by  the  electric  arc  has  been 
mostingeniouslyutilizedinthe  "Cowles  Electric  Furnace," 
by  means  of  which  corundum  and  other  refractory  oxides 
never  before  directly  reduced  are  made  easily  reducible. 
See  Mem.  of  Chemistry,  Appendix  25. 


[Elements  of  Natural  Philosophy,  pp.  347-349.]  171 

§468.  ■  The  currents  circulating  in  th<>  trlcphone  are  perhaps  a 
thousand  million  times  less  than  those  which  would  cause  an  ordi- 
nary electromagnet  to  attract  a  piece  of  soft  iron  close  to  its  pole 
vith  a  force  equal  to  a  few  grains." — Jenkin. 

Exercises,  Page  349. 

L  °  =  f  =  4.56  xT6  + 10:55  "  10-°4-  TheProWem 
ignores  the  resistance  of  the  line,  i.  e.,  assumes  that  the 
circuit  is  short  and  of  inconsiderable  resistance. 

2.  See  §  458. 

3.  C :  c  =  tan  m  :  tan  n     .\  9.925  :  c  —  tan  60°  :  tan  74°. 
.-.  9.925  :  c  =  1.73  :  3.49.     .-.  c  =  20  +  - 

4.  C  =  f  - .     .-.  1  =  ^.     .-.  R  =  30.     Ans.,  30  ohms. 

K  K 

5.  The  first  wire  has  a  weight  of  2.4  grains  and  a  resist- 
ance of  0.1  ohm  per  ft. 

The  second  wire  has  a  weight  of  1  grain  and  a  resist- 
ance of  x  ohms  per  ft. 

Resistances  are  inversely  as  weights  of  equal  lengths. 
1  grain  :  2.4  grains  =  0.1  ohm  :  x  ohms. 
.-.  x  =  .24. 

6.  1st  wire,  pure,  1  foot  long,  weighs  1  grain  and  has 
R  =  .2106  ohm. 

2d  wire,  if  pure,  1  foot  long,  weighing  8.2  grains  would 
have  R  =  .02568  ohm. 

3d  wire,  commercial,  1  foot  long,  weighing  8.2  grains 
would  have  R  =  .02735  ohm. 

•-g|g  =  . 939  or  93.9*. 

7.  The  resistance  of  the  series  of  lamps  will  be  250 
ohms.  That  of  the  wire  may,  then,  be  5  ohms.  This  is 
at  the  rate  of  25  ohms  per  1,000  ft.  No.  24  i<  the  nearest 
to  the  size  desired,  but  as  the  line  resistance  "  must  not 


172  [Elements  of  Natural  Philosophy,  p.  350.~\ 

be  more  "  than  5  ohms,  we  must  use  the  next  larger  size 
of  wire  or  No.  23. 

8.  The  resistance  of  the  lamp  circuit  will  be  2.5  ohms 
and  that  of  the  200  ft.  of  wire,  .05  ohms.  This  is  at  the 
rate  of  .25  ohms  per  1,000  ft.  The  difference  between  this 
desired  resistance  and  200  ft.  of  No.  4  wire  (B.  &  S.)  is 
inconsiderable  and  may  safely  be  ignored.  In  practice, 
the  difference  would  probably  have  been  ignored  in  a  case 
like  that  of  the  last  Exercise,  and  No.  24  wire  used. 

9.  1  ohm  -^-.051  ohm  =  19.60784. 
1000  ft.  x  19.60784  =  19,607.84  ft. 

10.  206  -f-  (1.6  +  25.4)  =  7.63,  the  number  of  amperes. 
§386. 

11.  (2.8  +  1.1  +  9.36)  x  14.8  =  196.248.     §  386. 

12.  It  is  not  running  fast  enough.  With  the  given  re- 
sistances, a  25  ampere  current  will  require  an  E.  M.  F.  of 
212.5  volts.  The  dynamo  must  be  "  speeded  up  "  so  as  to 
give  the  additional  12.5  volts. 

13.  81.58  -r-  29.67  =  2.75,  the  total  number  of  ohm 
2.75  ohms  —  1.14  ohms  =  1.61  ohms. 

14.  -7.5)157.5(9 

1575     4.58 


4.42.—  Ans. 

15.  See  App.  K  (3).  As  the  carbon  filaments  are  hot 
when  the  lamp  is  in  use,  the  hot  resistance  of  an  incan- 
descence lamp  is  of  more  importance  than  its  cold  resist- 
ance. (39.3  x  3  +  11.2)  x  1.2  =  154.92. 

16.  (39.3  H-  3  +  H.2)  X  1.2  =  29.16. 

17.  The  current  is  the  same  in  both  lamps.     §  385. 

(97  x  2  -f  12)  =  206,  the  number  of  ohms.  See  §  386. 
206  x  1  (the  number  of  amperes)  =  206,  the  number  of 
volts. 

18.  3.8  x  10  =  38. 


[Elements  of  Xat'iml  P/tilo.wphy,  p.  351.]  173 

19.  The  resistance  of  the  arc  4-  the  resistance  of  the 
helices,  etc.,  of  the  lamp  =  4.42  ohms. 

4.42  x  10  =  44.2. 

20.  The  line  wire  is  3,300  ft.  long.  Its  resistance  is  that 
of  (3,300  x  W  =)  3,437.5  ft  of  pure  copper  wire  of  the 
same  size.  The  greatest  resistance  admissable  is  S%  of  24 
ohms  =  1.92  ohms.  Let  x  =  the  required  diameter  in 
mils. 

3,437.5  ft.  of  wire,  x  mils  in  diameter  has  R= 1.92  ohms. 
3,437.5  ft.     u        1     "  "         "    72=34,068.75  ohms. 

—  =  17,744,  the  ratio  between  the  resistances  and, 

1.92 

therefore,  the  ratio  between  the  sectional  areas  of  the  two 
wires.     But  the  sectional  areas  are   proportional   to  the 

squares  of  the  diameters.     Vl 7,744  =  133,  the  ratio  be- 
tween the  two  diameters. 

1  mil  x  133  =  133  mils. 

21.  Ignore  the  resistance  of  the  line  wire. 

E  =  Cx  R  =  .112  x  (70  +  15  x  25)  =  49.84 

Consequently,  each  of  the  25  cells  of  this  battery  ha<\ 
an  E.  M.  F.  of  about  2  volts.  Now  consider  the  battery 
of  30  such  cells  and  the  two  lamps  in  series: 

0-*l:  ?*W A -on« 

"  R  "  15x*0  +  *0x2  ~  17  ~ 

22.  Doubling  the  area  of  the  plates,  halves  the  internal 
resistance  of  each  cell  but  has  no  other  effect.  §§  400, 
379  (2). 

E  _  2x30  2 

°-  R  ~  7.5x*0  4-*0x~2  =  ^5  =  °-2105- 

23.  The  length  of  the  actual  line  is  18,480  ft.  The 
length  of  a  similar  wire  of  pure  copper,  having  the  same 
resistance,  is  (18,480  f t.  x  W  = )  20,533 J  ft.  The  problem 
shows  that  0.1  of  the  resistance  of  the  external  circuit  is 
in  the  wire,  the  other  0.9  being  in  the  lamps  (§  470).    But 


174  [Elements  of  Natural  Philosophy,  pp.  851-353.] 


the  total  resistance  of  the  lamps  is  225  ohms.  Therefore, 
the  resistance  of  the  line  is  25  ohms,  the  total  external 
resistance  being  250  ohms. 

20,533^  ft.  of  pure  copper  wire,  diameter  required,  has 

R  =  25  ohms.. 
20,533£  ft.  of  pure  copper  wire,  diameter  of  1  mil.,  has 
R  =  204,101  ohms. 

— ~z —  =  8,164,  the  ratio  of  resistances  and,  therefore, 
of  sectional  areas. 


\/8,164  =  90.3,  the  ratio  of  diameters. 

1  mil  x  90.3  ss  90.3  mils. 
§  470.  A  wire  conveying  a  current  of  electricity  (or  a 
magnet)  is  capable  of  producing  mechanical  action  in  an- 
other wire  bearing  an  electric  current. 

Figure  A  represents  a  frame  devised  by  Ampere  for  the  purpose 
of  rendering  such  a  conductor  movable  without  an  interruption  of 


Fig.  A. 


Fig.  B. 


the  current  carried  by  it.  The  rectangular  wire  frame  is  supported 
by  the  two  pointed  ends  of  the  wire  which  rest  in  small  metallic 
cups  placed  one  above  the  other  in  the  vertical  axis  of  the  frame. 
The  upper  point  rests  on  the  bottom  of  its  cup,  and  carries  the  weight 
of  the  frame.  Both  cups  contain  mercury  to  render  perfect  the  elec- 
tric communication  between  them  and  the  ends  of  the  wire  frame. 
The  cups  are  carried  by  horizontal  metal  arms,  insulated  from  each 
other  and  supported  by  metal  posts  in  communication  with  the  bind- 


[Elements  of  Natural  Philosophy,  p.  353.] 


175 


ing  poets  as  shown  in  the  figure.     If  the  wire  frame  be  placed  in 

circuit,  and  a  magnet  placed  beneath  as  shown  in  Fig.  2?,  the  wire 

frame  will  assume  such  a  position  that  its  plane  will  be  perpendicular 

to  the  length  of  the  magnet.     The  experiment  is  the  converse  of 

that  described  in  §  417  of  the  text- book. 

If  no  magnet  be  used  other  than  the  earth  (§  437)  the  frame  will 

be  placed  so  that  its  plane  is  perpendicular  to  the  magnetic  meridian, 

and  in  such  a  manner  that  the  current  in  its  lower  side  is  from  east 

to  west.     The  current  will  then  be  upward  in  the  western  side  and 

downward  in  the  eastern  sid«\ 

For  the  purpose  of  showing  the  effect  of  one  current  upon  another, 

it  is  desirable  that  the  two  metal  posts  be  at  opposite  ends  of  the 

base  of  the  frame,  and 
the  frames  suspend- 
ed between  them,  as 
shown  in  Fig.  C.  In 
this  apparatus,  as  in 
that  described  above, 
the  posts  are  con. 
nected  with  wires 
from  a  battery,  con- 
nection between  the 
posts  being  made  by 
the  movable  frame. 
When  the  current  is 
passed  through  this 
apparatus,  the  frame 
is  placed  so  that  its 
plane   coincides  with 

that  of  the  two  pillars,  and  so  that  the  parallel  currents  in  either  side 

of  the  frame  and  its  adjoining  post  are  flowing  in  the  same  direction. 

If,  instead  of  the  frame  just  considered,  we 

use  one  the  wire  of  which  does  not  cross 

itself  at  a,  (Fig.  JD),  it  will  be  seen  that  the 

current  in  either  post  flows  in  a  direction 

opposite  to  that  of  the  current  in  the  adjoin- 

Ing   side  of   the  movable   frame.      In   this 

case,  the  frame  will   be  turned  away  until 

stopped  by  the  collision  of  tin*  win  s  in  the 

upper  part  of  the  apparatus.     In  using  the 

first  frame,  there  is  an  attraction  manif.  st. d 

between  the  post   v  and   the   side   fte,  and 

between  the  post  t  and  the  side  de  ;  in  using  the  second  frame  there 


Fig.  D. 


176 


\ Elements  of  Natural  Philosophy,  p.  353.] 


is  a  corresponding  manifestation  of  repulsion  instead  of  attraction. 

These  several  phenomena  may  be  summed  up  as  follows : 

Parallel  currents  flowing  in  the  same  direction  attract  each  other; 

parallel  currents  flowing  in  opposite  directions  repel  each  other. 

The  plates  of  a  Voltaic  Element  (See  p.  315)  may  be  floated  upon 

the  diluted  acid  by  means  of  a  cork,  the  connecting  wire  passing 

above  the  cork.     If  the  wire  from  another  circuit  be  parallel  to  the 

conducting  wire  of  this  floating  element  (called  De  la  Rive's  battery), 

the  law  above  given  may  be  verified.     A  spiral  coil  of  insulated  wire 

(a  helix)  may  be  placed  on  the  cork,  in  the  circuit  of  the  floating 

battery.     The  heiix  will  possess  the  properties  of  a  magnet.     The 

floating  helix  may  replace  the  magnet  of  Fig.  209. 

The  attraction  of  parallel  currents  flowing  in  the  same  direction 

may  be  shown  by  the  "  contracting  helix  " 

shown  in  Fig.  E.     A  spiral  of  fine  copper 

wire,  supported  as  shown,  is  connected  at  its 

upper  end  with  the  positive  pole  of  a  battery, 

and  just  dips  into  a  cup  of  mercury  connected 

with    the   negative    pole  of   the    battery. 

When  the  current  passes,  each  turn  of  the 

spiral  attracts  each  of  its  neighbors.     The 

spiral  is  thus  lifted  and  the  circuit  broken 

with  a  spark  at  the  surface  of  the  mercury, 

(§  407).       The  current   being  interrupted, 

gravity  draws  the  spiral  down  again,  and 

closes  the  circuit,  with  another  spark.    This 

circuit  is  thus  automatically  made  and  broken  by  the  up  and  down 

vibratory  motion  of  the  helix. 

A  solenoid  is  an  elongated  helix  with  the  ends  of  its  wire  carried 

back  until  they  nearly  meet  at  the  middle.     The  returning  wires  are 

sometimes  on  the  outside  of 
the  helix,  but  more  commonly 
in  its  axis.  A  solenoid  may 
be  suspended  from  Amperes' 
stand  as  shown  in  Fig.  F.  As 
each  loop  corresponds  to  the 
frame  represented  in  Figs.  A 
and  B,  the  passage  of  a  cur- 
rent will  cause  each  loop 
to  be  placed  perpendicular  to 
the  magnetic  meridian.  This 
means    that    the   axis  of   the 

solenoid  will  be  placed  in  a  north  and  south  line.     (Exp.  102.)    It  may 


Fig.  F. 


[Elements  of  Natural  Philosophy,  pp.  363-357.]  17? 

accordingly  be  said  to  have  +  and  —  poles.  If  it  could  be  sup- 
ported so  as  to  move  freely  about  its  centre  of  gravity,  it  would 
place  its  axis  parallel  to  that  of  a  dipping  needle  at  the  same  place. 
(See  Deschanel's  "  Natural  Philosophy,"  p.  692.)  Repeat  Experi- 
ment 83,  at  first,  with  a  bar  magnet,  and  a  solenoid  suspended  from 
Ampere's  stand  ;  and  'secondly,  with  two  solenoids  as  shown  in 
Fig.  F.  In  the  latter  case,  the  reason  for  the  attraction  or  repulsion 
may  be  made  more  clear  by  placing  the  solenoids  end  to  end  and 
noticing  that  when  unlike  poles  are  placed  opposite,  we  have  parallel 
currents  flowing  in  the  same  direction  and,  hence,  attraction  ;  that 
when  like  poles  are  placed  opposite  we  have  parallel  currents  flowing 
in  opposite  directions  and,  hence,  repulsion.  A  pole  changer  for 
Ampere's  stand  or  other  uses  is  described  in  Frick's  "Physical 
Technics,"  p.  376  (§§  317,  318).  Also  see  the  following  paragraph. 
g  319. 

§  471.  A  joule  measures  the  work  done-  by  a  coulomb 
falling  through  a  difference  of  potential  of  a  volt ;  it  is  a 
volt-coulomb.     We  copy  the  following  for  reference : 

(0.101937  kilogrammeters. 
0.737324  foot-pounds. 
0.24067  lesser  calories. 
107  ergs. 
1  kilogrammeter  =  9.81  joules  ;  1  foot-pound  =  1 .35626  joules. 

§473.  See  Frick's  "Physical  Tech nics,"  p.  373  (§315) 
and  p.  382  (§  321). 

§  475.  We  copy  the  following  for  reference  : 

0.00134059  horse-power. 

0.101937  kilogrammeters  per  second. 

6.11622  kilogrammeters  per  minute. 

0.00024067  calories  per  second. 

0.24067  lesser  calories  per  second. 

0.144402  calories  per  minute. 

107  ergs  per  second. 
1  horse-power  =  745.941  watts. 
1  kilogrammeter  \*  r  second  =  9.81  watts. 
1  foot-pound  per  second  =  1.35626  watts. 


1  watt  (or  volt-ampere) 


178  [Elements  of  Natural  Philosophy.] 

Exercises,  Page  359. 

1.  A  watt. 

2.  W  =  C*R  =  100  x  44.76  =  4,476. 
4,476  -T-  746  =  6. 

3.  §  471.    Joule  =  C*Rt  =  100  x  442  x  60  =  26,520 

4.  H  =  &Rt  X  0.24  =  1.44  x  40  x  60  x  0.24  =  829.44, 
the  number  of  lesser  calories.  But  it  takes  1,000  lesser 
calories  to  make  1  calorie.  Hence,  the  answer  is  0.82944 
calories.  If  a  pupil  says  that  he  does  not  kuow  what  a 
calorie  or  a  lesser  calorie  is,  remind  him  that  the  index  will 
refer  him,  in  either  case,  to  §  579,  and  that  the  index  was 
made  for  just  such  ends. 

5.  F.  P.=  C2Rt  x  0.737335=25  x  100  x  60  x  0.737335  = 
110,600.25. 

o      rrr         n         n  n  W  30>000 

6.  W=CxE    .,C=-=J^-  =  10. 

7.  W  =  C  x  E  =  10  x  45.2  =  452,  the  number  of 
Watts  or  about  f  H.  P. 

8.  25  x  37.7  =  942.5. 
942.5  -T-  746  =  1J. 

9-  w  °  =  i  =  m  =  °-88- 

(b.)  H=  C*Rt  x  0.24  =  (0.88)2  x  125  x  1  X  0.24= 
23.232. 

10.   (a.)  1.9  -r-  3.4  =  0.559. 

1.9  -r-  30.4  =  0.0625. 

(b.)  J  =  C*Rt  =  (.559)2  x  o.4  x  1  =  0.12499. 
(.0625)2  x  0.4  x  1  =  0.00625, 


[Elements  of  Natural  ffjUfctqpAgf  ]  K'J 


Review  Questions,  Page  301. 

4.  (b.)  By  mechanical  action  (§  372) ;  by  chemical  action 
(§  373)  and  by  induction  (§  456). 

m     .    .  1014  x  40002        W4  x  ^000 

6-  <"•>  '  "T200*—  =  -  IT  "  =  60°- 

***  J^.,  600  1b. 

(J.)  See  §  254(c)/  ^4 ns.,  72.18  ft  (c.)  4  =  .714  + .— ^w». 

7.  See  §  128.  S  =  \gP\  3,600  =  16.08/2 ;  t  =  14.96  + . 
v  =  gt  =  32.16  x  14.96  +  =  481.2  — ,  the  velocity  in 
feet.  Before  finishing  the  solution,  it  may  be  well  to  pro- 
duce a  new  formula  for  getting  the  velocity,  in  such  a  case 
as  this,  by  a  more  direct  method. 

v  v* 

v  =  qt\  t  =  -;  t?  =—  .    Substitute   this   value  of   fl 

y  9  f 

av1         v2 
m  the  formula:  S  =  igf2;    S  =  jgj  =  5-;  v*  =  2gS; 

v  as  y/2g&.     (See  §  254  c.)    Using  this  formula, 

v  =  VfyS  =  a/64.32  x  3,600  =  V23 1,552  =  481.19  + 
as  previously  obtained  by  the  other  method. 

K.  E  =  2?  (§  157)  or  K.  E.  =  w  ^  j*      (See  Note 

on  page  130  of  this  Hand-Book.)     Using  this  last  formula, 

/481  2\2 
K.  E.  as  25  ljj£)  =  25x602  =  25x3,600  =  90,000, 

the  number  of  foot-pounds. — Ans. 

N.  B. — Some  of  your  pupils  will  probably  solve  this  problem  in 
some  such  way  as  that  given  above.  Possibly,  none  of  them  will 
do  it  more  directly.  In  even  such  a  case,  the  young  teacher  need 
not  feel  discouraged;  the  experienced  teacher  will  not.  Give  the 
class  the  new  formula,  and  have  them  use  it  in  solving  the  problem. 


180  {Elements  of  Natural  Philosophy,  pp.  361-366.] 

Then  show  tliem  what  they  lost  by  failing  to  apply  general  prin- 
ciples. Have  them  re-read  §  159  and  lead  them  to  see  that  the  hall's 
kinetic  energy  at  the  end  of  its  fall  was  due  to  the  potential  energy 
with  which  it  began  its  fall  and  was  equal  to  it,  and  that  it  would 
lift  the  weight  to  exactly  the  height  from  which  it  fell.  But  the 
energy  necessary  to  lift  this  25  lb.  ball  3,600  ft.  high  is  (25  x  3,600=) 
90,000  foot-pounds  (§  153,  a). 

9.  27  in.  x  13.6  =  367.2  in.  or  30f  tL—An*. 

10.  (c.)  See§  238. 

11.  (a.)  See  §§  254,  256.  8.02y77  =  40.1,  the  velocity 
per  sec.  expressed  in  feet.     40.1  ft.  =  481.2  in.     2  cu.  in. 

x  481.2x3,600  =  3,464,640  cu.  in.  3,464,640  -i-  231  = 
14,998.44,  the  number  of  gallons. — Ans. 

14.  (c.)  Either  coat  may  be  -f,  the  other  coat  being  — 

15.  (a.)  The  chemical  changes  (§  373)  involved  in  the 
growth  of  vegetation  has  been  claimed  as  one  of  the  causes 
of  atmospheric  electricity.  It  is  well  known  that  thunder- 
storms are  much  more  frequent  in  summer  than  in  winter. 

16.  See  §§  430,  454. 

18.  See  note  in  this  Hand-Book  on  Ex.  7,  p.  328  of 
text-book. 

25.  See  note  on  p.  L83  of  text-book  ;  §  324  (b)  and 
Exp.  20. 

27.  (a.)  The  62  grains  of  air  measures  200  cu.  in.  (§272.) 
£  of  200  cu.  in.  =  160  cu.  in.     (b.)  \  of  200  cu.  in.  = 

40  cu.  in.      (c.)  49.6  gr.   x   U)  =  16.2529+  grains.    See 

4\5 


§  289.     (d.)  15  lb.  x  ( g)  =  4.9152  lb.      (e.)  1    Kg. 

(f\5  =  .32768  Kg.  or  327.68  g.     (/.)  30  in.  x 

9.8304  in. 

28.  (a.)  No.     (b.)  The  charge  of  each  inner  coat  wil 
be  "  bound  "  by  the  charge  of  the  outer  coat. 


[Elements  of  Natural  Philosophy,  p.  363.]  181 

.61 

2 

29.  For  pressure  on  the  bottom  :  62.5  lb.  xl.tt  x  *   = 

76.25  lb.     For  pressure  on  either  side:   The  imaginary 

(2       1      \  2 
3  X  3      /  9CU*  ft*     62'5  lb#   X 

.61 

1M  X  |  =  25.42-  lb. 

3 

30.  25  lb.  x  6  x  100  =  15,000  lb.— Arts.  * 

31.  H04  (*).!=!  +A+B-  •••^  =  4-1^ 
the  number  of  ohms. 

32.  (c.)  In  a  straight  line. 

33.  (c.)  15  lb.  x  U  =  12  lb.  ^w*.,  12  lb.  per  sq.  in. 
1  Kg.  xtt  =  -8  A£.  or  800  g.    Arts.,  800  #.  per  sq.  cm- 

34.  («.)  The  room  contains  6,000  cu.  ft.  or  10,368,000 
cu.  in.  (See  §  272.)  .31  grains  x  10,368,000  =  3,214,080 
grains  or  459.15  lb.  Av. — A?is. 

35.  The  1,000  cu.  cm.  flask  contains  700  cu.  cm.  of  water. 
The  300  cu.  cm.  of  mineral  weighs  750  grams.  An  equal 
bulk  of  water  weighs  300  g.    750  g.  ■+■  300  g  =  2.5  —  Am. 

36.  The  tank  contains  1  cu.  m.  or  1,000  I.  of  water.  Each 
liter  of  water  weighs  1  Kg.  The  1,000  liters  weigh  1,000  Kg., 
the  pressure  on  the  bottom.  The  pressure  on  any  side  will 
be  one-half  as  much;  the  imaginary  column  (§§  226, 
231)  has  the  same  base  but  only  half  the  altitude  that  it 
has  in  the  case  of  downward  pressure. 

OQ  ,  ,  .031  x  242  .022  x  18*  "  ,  ., 
38.  (a.)  — -—  +  — —  =  1.27 +,  the  num- 
ber of  kilogrammeter8.  (b.)  The  first  has  a  momentum 
of  U  x  31  =)  744;  the  second  has  a  momentum  of 
(18  x  22  =)  396.  The  momentum  after  impact  is 
(744  —  396  =)  348.  The  weight  being  now  53  grams, 
the  velocity  will  be  348  -7-  53  =  6.566+  m. 

the  kinetic  energy  expressed  in  kilogram  meters. 


182 


[Elements  of  Natural  Philosophy,  pp.  361-366.'] 


39.  (a.)  The  same  as  38  (a).  See  problem  above,  (b.) 
7444.366  =  1,140,  the  momentum  after  impact.  1,140  -~ 
53  =  21.5,  the  velocity  after  impact. 

w*  _   .053  x  21.5»  _ 

*  E-  ~  W TSF^  ?  -  L25' 

the  kinetic  energy  expressed  in  kilogram  meters. 

40.  (a.)  See  Fig.  102.  (c)  (|)4  =  fff  or  .4096,  the  part 
of  the  air  originally  in  the  receiver  that  now  remains,  {d.) 
It  will  be  Iff  times  as  great. 

41.  Sin  9°  :  sin  70°  =  j  :  x. 

.156  :  .940  =  %:x    .:  x  =  1. 

42.  A  Leyden  jar.  The  charged  ball  represents  the 
inner  coat. ;  the  dry  air  is  the  dielectric ;  the  walls  of  the 
room  represent  the  outer  coat. 

44.  1  ft.  of  the  first  wire,  pure,  weighs  1  grain  and  has 
R  ss  0.2106  ohm. 

1  ft.  of  the  second  wire,  if  pure,  would  weigh  7.5  grains 
and  have  R  =  0.02808  ohm. 

1  ft.  of  the  second  wire,  commercial,  weighs  7.5  grains 
and  has  R  =  0.03065  ohm. 

0.02808  -r-  0.03065  =  0.916  or  91.6^. 

45.  Let  the   pupils  wrestle  with   this  for  a  fortnight 


before  you  help  them  with  the  following.    If  no  one  gets 
it,  you  must  not  be  disappointed. 


[Elements  of  Natural  Philosophy,  pp.  361-366.]  183 

In  the  accompanying  diagram,  the  two  ends  of  the  lin-*  win-  ar«- 
connected  with  "  three  point  switches,"  one  of  which  consists  of  th  • 
metal  bit,  it  in,  pivoted  to  the  binding  post,  a,  and  the  two  binding 
posts,  c  and  e.  The  push  button,  P,  and  the  ball,  A,  may  be  n-spect- 
ively  replaced  by  telegraphic  key  and  sounder.  The  connections 
with  line,  battery,  earth,  etc.,  are  sufficiently  shown  in  the  diagram. 
When  the  line  is  at  rest,  m  is  turned  into  contact  with  0  and  it  into 
contact  with  r.  If  the  operator  at  the  left  wishes  to  send  a  signal  or 
a  message,  he  turns  his  switch  from  c  to  e  and  operates  the  button 
or  key  at  P.  The  current  passes  from  B,  via  P,  e,  a,  line,  i,  r,  A' 
(giving  signal),  and  earth  back  to  B,  while  B'  is  open  circuited  atP' 
and  s.  When  he  has  finished,  he  turns  m  back  to  r.  Then  the  other 
operator  may  turn  n  to  s  and  signal  at  P',  the  current  passing  from 
'  *,  i,  a,  c,  A  (giving  signal)  and  earth,  B  being  open  circuited 
at  P  and  e.  The  switch  is  not  essential,  of  course,  but  it  affords  an 
easy  means  of  changing  the  connections  at  the  ends  of  the  line. 

46.  H=  C*Rt  x  0.24  =  (0.14)2  x  4  x  GOO  x  0.24= 11.2896, 
the  number  of  lesser  calories. 

48.  The  internal  resistance  should  be  as  near  12  ohms 
(the  external  resistance)  as  possible.  The  48  cells  may  be 
placed  in  series,  in  which  case  the  internal  resistance  of 
tbe  battery  will  be  96  ohms.  Or  they  may  be  in  a  series  of 
24  groups  each  of  2  cells  abreast,  with  an  internal  resist- 
ance of  24  ohms ;  in  a  series  of  16  groups  of  3  abreast 
with  a  resistance  of  lOf  ohms ;  in  a  series  of  12  groups  of 
4  abreast  with  a  resistance  of  6  ohms,  and  so  on  with  series 
of  8,  6,  4,  3  and  2  groups  or  in  a  battery  of  48  cells  abreast, 
the  resistance  continually  getting  further  and  further 
away  from  the  desired  12  ohms  after  we  pass  the  third 
arrangement,  namely,  of  16  groups,  each  of  3  cells  abreast 

E 

49.  R  =   p  =  83.568,   the   total    resistance  in   ohms. 

From  this, deduct  in g  the  external  resistance  (4.51  x  16  4-0.8), 
we  have  left  10.608  ohms. 

50.  See  §  356. 


184  [Elements  of  Natural  Philosophy,  pp.  361-366.'] 

51.  Sound,  light  and  heat. 

52.  H=  Cmt  x  0.24=100  x  50  x  900  x  0.24=1,080,000, 
the  numher  of  lesser  calories.     This  equals  1,080  calories. 

53.  A  watt  is  a  volt-ampere  and  equals  y^g-  H.  P.     §  475. 

140  x  9 -=-746  =  1.69. 

54.  Each  series  of  3  cells  has  an  internal  resistance  of  12 
ohms.  The  battery  of  two  such  series  placed  abreast  has 
an  internal  resistance  of  6  ohms.     See  §  402. 

55.  The  increase  in  the  length  of  the  wire  increases  the 
external  resistance  36  fold  and  thus  decreases  the  current 
strength.  This  must  be  provided  for  by  increasing  the 
E.  M.  F.,  or  by  decreasing  the  internal  resistance  so  as  to 
keep  the  current  up  to  its  original  strength.  In  either 
case,  a  greater  number  of  cells  is  needed. 

56.  (a.)  2.628  ohms  x  16.743  =  44  ohms. 
5.5 


E       11 

57.  C  =  -=  =  .— .     The  current  will  be  greatest  when 

it        Z.Z 

the  external  resistance  is  so  small  that  it  may  be  ignored. 
Hence,  with  a  single  cell,  the  maximum  current  strength 

will  be  j  ^  =  J  0.5  amperes.     Now,  increase  the  battery 

to  any  number  of  cells  in  series.     Eepresent  this  number 

by  n.     Then   the  current  strength  will  be  ~— =  0.5. 

ii .  4/  X  'Yl 

q.  e.  d.  It  may  be  clearer  to  some  pupil  if  he  be  required 
actually  to  assign  definite  values  to  n,  such  as  5,  200, 
1,000,000,  etc.,  in  succession,  and  cancel  from  numerator 
and  denominator,  the  equal  factors  thus  introduced. 

58.  W  —  C  x  E  =  10.04  x  838.44  =  8,417.9376. 

8,417.94  -h  746  =  11.28.  §  475. 

60.  (a.)  There  being  1,000  lamps   of   equal  resistance 
placed  abreast,  each  will  take  y^q  of  the  total  current 


[Elements  of  Natural  Philosophy,  pp.  365,  366.]  185 

See  §  404.      If  each  lamp  gets  1  ampere,  the  total  current 
must  be  1,000  amperes. 

(b.)  50  ohms  -r-  1,000  =  0.05  ohms. 

(c.)  The  electromotive  force  must  be  enough  to  send  a 
1  ampere  current  through  the  50  ohms  resistance  of  each 
lamp.     E  =  C  x  R  =  1  x  50  =  50,  the  number  of  volts. 

(d.)  The  external  resistance  is  0.05  ohms  and  the  total 
resistance  is  0.055  ohms.  The  total  current  is  1,000 
amperes. 

E  =  C  x  R  =  1,000  x  0.055  =  55. 

(e.)   W  =  E  x  C  a  50  x  1  =  50. 

(/.)  This  will  leave  500  of  the  50  ohm  lamps  abreast 
50  -j-  500  =  0.1. 

(g.)  The  total  E.  M.  F.  is  55  volts,  as  above  ascer- 
tained (d). 

The  total  resistance  is  now  0.1  +  0.005  =  0.105. 

C=l  =  oS>5  =  523-81- 
(h.)  523.81  amperes  -r-  500  =  1.0476  amperes. 

61.  The  resistance  of  the  lamp  circuit  is  48.9  ohms, 
which,  added  to  the  20  ohms  resistance  of  the  battery,  gives 
68.9  ohms  as  the  total  R  of  the  circuit. 

E  =  Cx  R  =  1.16  x  68.9  =  799.24,  the  total  E.  M.  H 
(in  volts)  of  the  40  cells.  799.24  volts  -5-  40  =  1.998 
volts,  the  E.  M.  F.  of  each  cell. 

A  series  of  60  such  cells  would  give  an  E.  M.  F.  of  1.998 

volts  x  60  =  119.88  volts  and  have  an  internal  resistance 

of  30  ohms  (}  ohm  per  cell).     The  total  resistance  of  the 

circuit  now  is  (16.9  +  32  +  20  +  16  +  30  =)  114.9  ohms. 

C_E_  119,88 

°  -  R  -    114.9    -  1M3' 

62.  This  would  have  halved  the  internal  resistance  of 
the  battery. 

C  =  !L  -  U9'SS  -  1  2 

"  R  "  16.9  +  32  +  20  +  16  +  15  "~ 


186  [Elements  of  Natural  Philosophy,  p.  366.] 

63.  W  =  ClR  =  102  x  83.5  =  8,350,  the  number  of 
Vatts.     §  475. 

8,350  -J-  746  =  11.19,  the  number  of  electrical  H.  P, 
11.19  +■  15.3  =  0.73  or  73^. 

73 

64.  11.19  H.  P.  x  snr  =  9.77  H.  P. 

Od.  0 

9.77  -7-  15.3  =  0.64  or 


CHAPTER  VII. 

§  477.  Do  not  fail  to  get  Mayer's  little  book  on 
"Sound."  See  Experiment  58,  therein.  See  p.  23 
herein. 

§  478.  See  Frick's  "  Physical  Technics,"  p.  163  (§  133). 

§  481.  See  Dolbear's  "The  Telephone,"  p.  G4. 

§483.  See  First  Prin.  Nat.  Phil,  Exps.  139,  140; 
Pickering's  "Physical  Manipulation,"  p.  125  and  Desch- 
anel's  "Natural  Philosophy,"  §  629. 

§  484.  See  First  Prin.  Nat.  Phil,  Exps.  141-144  and 
Daniell's  "  Principles  of  Physics,"  p.  429. 

§  485.  "  It  is  marvellous  how  slight  an  impulse  throws  a  vast 
amount  of  air  into  motion.  We  can  easily  hear  the  song  of  a  bird 
500  ft.  above  us.  For  its  melody  to  reach  us,  it  must  have  filled  with 
wave  pulsations  a  sphere  of  air  1000  ft.  in  diameter,  or  set  in  motion 
18  tons  of  the  atmosphere." — Youmans. 

§  487.  Experiments  made  at  the  U.  S.  Arsenal  at 
Watertown,  Mass.,  go  to  show  that  the  velocity  of  sound 
depends  to  some  extent  on  the  intensity  and  that  ordinary 
determinations  of  the  velocity  of  sound  (cannon  being  used 
to  produce  the  sound)  contain  an  error,  due,  perhaps,  to 
the  bodily  motion  of  the  air  near  the  cannon. 

§  488.  In  182G,  at  Lake  Geneva,  two  boats  were  moored 
at  a  distance  of  13,500  in.  (between  8  and  9  miles)  from 
each  other.  From  one  boat,  a  bell  was  hung  in  the  lake. 
By  a  simple  contrivance,  a  quantity  of  gunpowder  was 
ignited  in  the  air  at  the  instant  when  the  hammer  struck 
the  bell  in  the  water.  The  other  boat  had  a  trumpet 
lhaped  tube  with  its  lower  opening  covered  with  a  mem- 
brane  and  facing,  under  water,  toward  the  first  boat  and  the 
bell.     An  observer,  with  his  ear  at  the  upper  end  of  the 


188  [Elements  of  Natural  Philosophy,  pp.  373,374.] 

hearing  trumpet,  noted  the  interval  between  seeing  the 
flash  and  hearing  the  sound.  He  found  the  velocity  of 
the  sound  in  water  to  be  1,435  m.  per  second  or  more  than 
four  times  its  velocity  in  air.     See  §  653,  c. 

If  a  pressure  of  x  dynes  per  sg.  cm.  applied  to  a  fluid  produces 

a  compression,  y  {i.e.,  reduces  unit  volume  of  the  fluid  to  volume 

x 
1  —  y),  then  is  -  called  the  coefficient  of  elasticity  of  that  fluid.     In 

if 

the  formula,  given  in  the  text- book,  this  is  represented  by  i?  and  the 
density  of  the  fluid  by  D. 

§  488  (a).  It  may  be  well  to  give  the  following  problems 
to  the  class,  one  daily: 

Chlorine  gas  is  about  36  times  as  heavy  as  hydrogen. 

(a.)  In  which  gas,  under  the  same  atmospheric  pressure,  will  sound 
travel  the  faster?     (b.)  How  many  times  as  fast? 

Ans.  (a. )  In  hydrogen,  the  lighter  gas.  (b.)  The  tension  or  elas- 
ticity, being  the  same  in  both  cases,  need  not  be  considered. 

^36  =  6. 

If  a  body  of  gas  be  subjected  to  a  pressure  of  two  atmospheres 
instead  of  one,  its  volume  will  be  halved  ;  its  density  and  its  tension 
or  elasticity  will  be  doubled.  Will  sound  travel  through  air  thus 
compressed  with  greater  or  with  less  velocity  than  it  does  through 
the  ordinary  atmosphere,  the  temperature  being  the  same  ? 

Ans.  There  will  be  no  change  of  elasticity  arising  from  the  change 
of  temperature.  The  act  of  compression  would,  as  a  matter  of  fact, 
heat  the  air,  but  the  conditions  of  the  problem  require  that  time  be 
given  for  it  to  cool  down  to  the  original  temperature.  The  loss  of 
velocity  due  to  doubling  the  density  will  just  balance  the  gain  due  to 
doubling  the  tension. 

If  an  unconfined  body  of  gas  be  heated,  its  elasticity  is  unchanged 
but  its  density  is  lessened.  How  will  such  heating  affect  the  velocity 
of  sound  transmitted  by  the  gas  ?    Ans.  It  will  increase  it. 

If  a  confined  body  of  gas  be  heated,  its  elasticity  is  increased  but 
its  density  is  unchanged.  How  will  such  heating  affect  the  velocity 
of  sound  transmitted  by  the  gas  ?    Ans.  It  will  increase  it. 

Given  two  gases.     The  elasticity  and  density  of  the  first  are  to  be 


\/\~,A 


[Elements  of  Natural  Philosophy,  pp.  $74,  376.]  189 

considered  as  standards  (or  unity).  The  second  has  a  density  of  27  ; 
it  is  confined  and  heated  until  its  elasticity  is  3.  Sound  moves 
through  the  first  with  a  velocity  (c)  of  1,200  ft.  per  second.  I  want 
to  find  the  velocity  (  V)  of  sound  in  the  other  gas.  I  proceed  as 
follows : 

r :  F=  y\   :  |/§  ;    or,  1,200  ft.  :  V  =  f/j    :  f/~  .  or 

1,200  ft.  :  V  =  1  :  i-    Therefore,  V  =  400  ft. 

State  the  principle  that  underlies  my  solution.  Ans.  See  the 
second  sentence  in  §  488.  In  some  classes,  it  may  be  well  to  give  the 
problem  and  withhold  the  solution.  Each  teacher  can  tell  which 
plan  will  be  the  better  for  his  class.  It  is  not  well  to  assign  any 
problem  when  you  know  that  no  member  of  the  class  can  solve  it. 
This  applies  to  any  problem  in  the  text-book  as  well  as  here. 

§  491.  "  Practically,  musical  and  unmusical  sounds  often  shade 
insensibly  into  one  another.  The  tones  of  every  musical  instrument 
are  accompanied  by  more  or  less  of  unmusical  noise.  The  sounds  of 
bells  and  drums  have  a  sort  of  intermediate  character ;  and  the 
confused  assemblage  of  sounds  which  is  heard  in  the  streets  of  a  city 
blends  at  a  distance  into  an  agreeable  hum." — Deschanel. 

§  493.  A  valued  correspondent  writes  to  the  author  as 
follows: 

"  None  of  the  Philosophies  make  any  distinction  between  loudness 
and  intensity  of  sound.  *  *  *  *  Now  it  is  true  that  intensity 
depends  on  amplitude  and.  otlver  thingsbeing  equal,  loudness  depends 
on  intensity  and,  of  course,  on  amplitude.  But  a  viol  string  at- 
tached to  a  block  of  lead  of  the  size  of  the  viol  may  have  the  same 
amplitude  as  when  attached  to  the  violin,  but  the  loudness  is  far 
inferior.  (§  510.)  There  exists  the  same  distinction  between  quan- 
tity and  intensity  as  in  electricity.  Attached  to  the  violin,  the  whole 
of  the  wood  vibrates,  though  with  no  greater  amplitude  than  the 
string,  or  even  with  less,  but  the  quantity  of  tone  is  far  greater.  So 
Tyndall's  deal  rod,  reaching  down  to  the  sounding-board  five  stories 
below,  had  as  much  amplitude  of  vibration  and  as  much  intensity  of 
sound  as  when  a  violin  was  laid  on  its  upper  end.  but  the  quantity 
(and  loudness)  was,  in  the  former  case,  small  and  in  the  latter  large. 
So  a  battery  of  large  cells  is  related  to  a  battery  of  small  cells.  An 
intensity  battery  (§  400,  b)  of  ten  cells  gives  more  power  to  an 
electro-magnet  than  a  single  cell  does,  notwithstanding  magnetic 


190  [Elements  of  Natural  Philosophy,  pp.  375>  ^76-] 

power  is  said  to  depend  on  quantity.  In  fact,  it  depends  on  both 
quantity  and  intensity.  So,  loudness  is  the  result  of  both  intensity 
and  quantity  in  the  vibrations  of  the  air  or  other  medium  of  sound. 
I  have  a  glass  bell  which  yields,  to  the  viol  bow,  a  painfully  intense 
sound  which  is  yet  not  at  all  loud.  Some  bass  viols  yield  a  great 
quantity  of  sound  (like  some  human  voices)  which,  after  all,  pene- 
trates but  a  short  distance  and  sounds  ■  hollow  '." 

J.  D.  Everett  says  : 

"  The  loudness  or  intensity  of  a  sound  is  measured,  physically,  by 
the  amount  of  energy  which  it  communicates  to  the  ear  in  a  given 
time  and  this  energy,  in  comparing  two  simple  sounds,  is  propor- 
tional to  the  square  of  the  amplitude  of  the  particles  of  air  in  the 
neighborhood  of  the  ear.  But  from  the  point  of  view  of  sensation, 
this  rule  of  comparison  can  be  admitted  only  when  the  two  simple 
sounds  compared  are  of  the  same  pitch,  for  the  ear  is  unequally 
sensitive  to  simple  sounds  of  different  pitches.  Sounds  may  be  so 
high  in  pitch  as  not  to  be  heard  at  all  by  the  human  ear.  (See  note 
in  this  Hand-Book,  on  §  496.)  And,  within  the  limits  of  audibility 
there  is  considerable  difference  in  sensibility.  Within  the  range  of 
pitch  employed  in  music,  the  ear  is  more  sensitive  to  sounds  of  high 
than  of  low  pitch,  that  is  to  say,  the  same  amount  of  energy  of  aerial 
vibration  produces  a  more  intense  sensation  when  the  pitch  is  high 
than  when  it  is  low.  Of  two  compound  tones  of  equal  energy,  that 
which  is  strongest  in  high  harmonics  (§  527)  will  generally  affect  the 
ear  the  most." 

We  quote  from  another  author  : 

"The  sensible  loudness  of  sounds  does  not  coincide  very  closely 
with  their  physical  intensity.  This  arises  partly  from  modification 
in  the  form  of  the  vibration  induced  by  so  complicated  a  transmis- 
sion through  the  auditory  apparatus  and  partly  from  causes  purely 
physiological." 

§  494.  Suppose  a  bell  to  be  struck.  Aerial  waves  are 
started  in  every  direction,  as  spherical  shells.  At  a  certain 
instant  one  of  these  waves,  say  the  first,  has  travelled  5  ft. 
It  then  forms  the  surface  of  a  sphere  whose  radius  is  5  ft. 
Subsequently  the  wave  has  travelled  10  ft.,  when  it  forms 
the  surface  of  a  sphere  whose  radius  is  10  ft.  At  the 
second  instant,  the  energy  of  the  wave  is  spread  over  four 


[Element*  of  Natural  Philosophy,  pp.  376,  877.]         19 1 

times  as  much  surface  as  it  was  at  the  first  instant.  Hence 
the  amount  of  energy  represented  by  any  given  surface 
(e.  g.,  the  tympanum  of  the  ear)  will  be  only  one-fourth 
as  great,  or  the  sound  will  be  one-fourth  as  loud  at  the 
second  instant  as  at  the  first.  (It  is  a  well-known  geo- 
metrical truth  that  similar  surfaces  are  to  each  other  as 
the  squares  of  their  homologous  parts.)  This  argument 
assumes  that,  in  the  propagation  of  sound,  there  is  no  loss 
of  energy  ;  that  the  total  energy  of  the  larger  and  outer 
spherical  shells  is  the  same  as  that  of  the  smaller  and 
inner  shells.  This  cannot  be  strictly  true.  The  vibration 
implies  friction  and  condensation.  These  imply  the  gene- 
ration of  heat  at  the  expense  of  the  energy  that  produces 
the  vibrations.  (§  626.)  Consequently,  sonorous  energy 
diminishes  with  distance  somewhat  faster  than  according 
to  the  law  of  inverse  squares. 

The  loudness  of  a  sound  depends  also  upon  the  density 
of  the  air  in  which  the  sound  is  produced  ;  not  upon  the 
density  of  the  air  in  which  it  is  heard  (§  486  a.  and  b.). 
Aeronauts  find  that  when  their  balloons  have  reached  high 
elevations  they  have  to  speak  with  some  effort  to  be  heard. 
If  two  cannon  be  charged  equally  and  one  fired  in  the 
rarefied  air  at  the  top  of  a  mountain,  the  other  in  the 
heavy  air  at  the  foot  of  the  mountain,  the  first  may  be  un- 
heard by  the  gunners  in  the  valley  while  the  second  is 
plainly  heard  by  the  gunners  upon  the  mountain. 

§  496.  It  is  well  known  that  the  range  of  the  human 
voice  is  different  in  different  persons.  Some  sing  bass,  the 
rate  of  vibration  being  comparatively  slow  ;  others  sing 
the  higher  parts,  the  rate  of  vibration  being  quicker.  It 
is  equally  true,  though  not  equally  well  known,  that  the 
range  of  hearing  sounds  is  different  in  different  persons. 
Some  persons  are  unable  to  hear  low  sounds  which  are  not 
deficient  in  intensity  and  which  are  easily  recognized  by 
most  persons.  Others  are  unable  to  hear  acute  sounds 
which  are  audible  to  most  persons.     One  person  may  com- 


192  [Elements  of  Natural  Philosophy,  pp.  377-380.] 

plain  of  the  shrillness  of  a  sound  while  another  insists  that 
there  is  no  sound  at  all.  If  the  vibrations  be  fewer  than 
about  16  per  second,  the  sound  will  not  be  heard  continu- 
ously, that  number  of  vibrations  being  the  fewest  (or  the 
corresponding  wave  length  being  the  greatest)  that  can  be 
detected  by  the  human  ear.  Place  the  end  of  a  thumb  or 
finger  in  the  ear  ;  press  the  ends  of  the  fingers  of  the  same 
hand  forcibly  and  steadily  against  the  palm  ;  a  very  deep 
rumbling  tone  will  be  heard.  The  highest  tone  that  can 
be  detected  by  the  human  ear  consists  of  about  38,000 
vibrations  per  second. 

See  Mayer  on  "  Sound,"  p.  115,  and  Dolbear's  "  The 
Telephone,"  pp.  67-71. 

§  502  («).  See  First  Prin.  Nat.  Phil,  §  333,  a,  and 
Beechanel's  "Natural  Philosophy,"  §§  639-641. 

Note. — The  teacher  will  find  an  interesting  description  of  the 
iuman  ear  in  Daniell's  "  Principles  of  Physics,"  pp.  431-436. 


[Elements  of  Natural  Philosophy.]  193 

Exercises,  Page  3  SI. 

1.  82  —  32  =  50,  the  number  of  degrees  above  freez- 
ing point.  1.12  ft.  x  50  =  56  ft.  (§  489.)  1,090  ft.  + 
b6  ft.  =  1,146  ft.,  the  velocity  (§  487).  1,146  ft  x  18  = 
20,628  ft,  the  distance.— A  ns. 

2.  1,090  ft.  +  (2  ft  x  15)  =  1,120  ft,  the  velocity. 
See  §  4'.'<.<. 

3.  In  a  transverse  wave,  the  particles  move  across  the 
line  of  propagation  of  the  wave  ;  in  a  longitudinal  wave, 
the  particles  move  backward  and  forward  in  the  line  of 
propagation  (§  485). 

4.  1,150  ft  -  1,090  ft.  =  60  ft.  60  ft.  -j-  2  f t  =  30, 
t  he  number  of  centigrade  degrees  above  the  freezing  point 
(§  489.)— A  ns. 

502        25 

5.  (8  494.)   — :  =  — .      It  sounds  about  half  as  loud 

7   708        49 

to  B  as  it  does  to  A. 

6.  The  velocity  is  1,120  ft.  The  sound  required  3  sec. 
to  reach  the  cliff.     1,120  ft  x  3  =  3,360  ft— Ans. 

7.  The  velocity  must  be  1,100  ft.  per  sec.  (§482.)  This 
rekxaty  implies  a  temperature  of  5°  C. 

8.  (§  482.)  1,120  -~  4  =  280,  the  number  of  vibra- 
tions ;  15°  C. 

9.  332  m.  =  33,200  cm.  33,200  cm.  ~-  830=  40  cm.— 
Ans. 

10.  1,128  ft  i  8  ft  as  141 ;  1,128  ft.  +•  12  ft.  =  94. 
I  mm  141  to  94  vibrations  per  sec.  —  Ans. 

11.  It  took  the  sound  ^  sec.  to  reach  the  cliff.  The 
velocity  of  sound  at  the  ordinary  temperature  of  the  air 
(15°  C.)  is  1,120  ft.     ^  of  1,120  ft  =  210  ft.— Ans. 


194  [Elements  of  Natural  Philosophy,  p.  384.] 

§  505.  See  "  Nature/'  Vol.  XVIII,  p.  631,  on  the  "  Car- 
bon Telephone/'  The  "  Scientific  American  Supplement," 
No.  142,  tells  "How  to  Make  a  Working  Telephone."  For 
further  information  concerning  the  various  forms  of  tele- 
phones and  historical  accounts,  see  "  The  Speaking  Tele- 
phone," by  Prescott,  the  "Electrical  World"  (N.  Y.)  for 
April  10,  1886,  and  "Scientific  American  Supplements," 
Nos.  120,  128,  162,  163.  Toy  "telephones,"  in  which 
sound  waves  are  mechanically  transmitted  from  one 
station  to  the  other  maybe  bought  for  a  dime.  They  may 
be  made  easily.  See  First  Prin.  Nat.  Phil.,  Exp.  148. 
See  Mayer  on  "  Sound,"  Exp.  40.  Also  see  the  "  Scientific 
American,"  Vol.  XL,  p.  282,  and  Dolbear's  "The  Tele- 
phone," pp.  80-82,  and  103  et  seq. 

The  microphone  is  an  instrument  for  detecting  sounds  otherwise 
inaudible.  It  is  such  an  aid  to  hearing  as  the  microscope  is  to  seeing. 
Its  action  depends  upon  the  principle  involved  in  the  carbon  tele- 
phone, mentioned  above,  that  the  resistance  of  certain  electric  con- 
ductors is  diminished  by  an  increase  of  pressure.     The  microphone  is 


placed,  with  a  telephone,  in  the  circuit  of  a  galvanic  battery,  as 
shown  in  the  figure.  One  of  the  simpler  forms  consists  of  a  thin 
sounding-board,  a  b,  set  upright  on  a  wooden  base,  cd.  At  one  side 
of  the  sounding -boa;  i,  two  horizontal  metal  arms,  m  n,  carry  two 
blocks  of  gas  carbon,  e  i ;  a  rod  of  gas  carbon,  o,  with  pointed  ends, 
is  supported  in  cavities  in  the  opposite  faces  of  e  and  f.    The  arms, 


[Elements  of  Natural  Philosophy,  pp.  SSj-JM.]  1""> 

m  n,  are  fastened  to  a  6,  by  metal  screws,  communicating  with  the 
binding  posts,  d  f,  by  means  of  wires  on  the  other  side  of  the  sound- 
ing-board. By  means  of  these  screws,  tin-  arms  may  he  hold  in 
various  positions  on  a  6  and  held  either  firmly  or  loosely.  The 
ire  between  e  and  t  and  the  ends  of  o  may  thus  be  adjusted 
with  considerable  variety  and  delicacy.  Sound  waves  falling  upon 
n  t,  ntfW-t  the  pressure  upon  the  ends  of  o  and  thus  vary  tin*  resist- 
ance of  the  carbim  portion  of  the  circuit ,  that  is,  they  produce  rapid 
ions  in  the  current  passing  through  the  microphone.  These 
variations  in  the  current  cause  corresj)onding  vibrations  in  the  dia- 
phragm of  the  telephone,  T.  In  fact,  the  microphone  and  battery 
replace  the  transmitting  telephone  of  the  already  familiar  telephonic 
circuit. 

As  long  as  the  voice  is  the  sole  motive  power  of  the  apparatus,  as 
is  the  case  with  the  telephones,  it  is  evident  that  what  is  heard  at  the 
receiving  telephone  must  be  fainter  than  what  is  sjokeu  at  the  trans- 
mitting telephone  (§  165).  But  when,  as  in  the  case  of  the  micro- 
phone, the  energy  of  the  voice  is  used  merely  as  the  means  of  regu- 
lating the  strength  of  a  current  from  a  galvanic  battery,  there  is  no 
such  necessary  limitation  to  the  intensity  of  the  resulting  sound.  A 
small  boy  could  hardly  be  expected  to  lift  a  son  pile-driver  twenty 
feel  in  aminute,  but  he  may  work  the  throttle- valve  of  an  engine  that 
will  do  it.  The  sensitiveness  of  the  instrument  is  remarkable.  The 
circuit  being  closed,  the  drawing  of  a  fine  i)encil-brash  or  a  single  hair 
over  the  surface  of  a  b  produces  a  sound  that  is  very  plainly  audible. 
The  one  who  draws  the  brush  or  hair  hears  nothing  ;  the  listener  at 
the  telephone,  in  another  room,  may  be  startled  by  the  sound  he 
hears.  It  is  said  that  three  nails,  placed  in  a  circuit  so  that  the  ends 
of  one,  representing  o,  shall  rest  upon  the  ends  of  two  representing 
vi  e  and  n  i,  constitute  a  microphone.  The  microphone  has  been 
made  so  as  to  reproduce  articulate  sounds.  See  "  Scientific  American 
Supplements,"  Nos.  137,  163. 

'•  T«»  show  the  production  of  induced  currents  in  a  telephone  and 
tln-ir  physiological  effect,  attach  the  ends  of  the  wires  from  a  Bell 
nl.phone  to  the  leg  muscles  of  a  frog  (£  408)  and  speak  in  the  tele- 
phone. The  pronouncing  of  the  word  'sucker'  causes  the  leg  to 
move  or  '  jump  '  while  '  lie  still '  has  scarcely  a  perceptible  effect." 

I  &  On  tlie  phonograph,  see  "  Scientific  American  Sup- 
plements," Nos.   11$,  134,  ami  Miwr-m  ••  Sound,"  p.  170. 
I  Bftfc  See  DolbeaPs  "  The  Telephone,"  pp.  72-75. 
Many  sounds  may  be  transmitted  by  the  same  air,  at  the 


196  [Elements  of  Natural  Philosophy,  p.  390,  391.] 

same  time,  without  destroying  or  affecting  each  other.  An 
orchestra  of  fifty  pieces  would  probably  send  to  the  ear 
fifty  series  of  sound  waves,  each  different  from  the  other 
in  rate  and  amplitude  of  vibration,  etc.  Any  attempt  to 
imagine  the  resultant  motion  of  any  particular  air  particle 
due  to  these  fifty  separate  forces  would  be  bewildering. 
Yet,  from  this  "  aerial  entanglement "  the  ear  extracts 
order,  and  is  able  to  detect  and  follow  the  sounds  of  any 
one  instrument.  Still  we  must  remember  that  the  ear  may 
be  stunned  by  a  loud  sound,  so  as  to  be  unable  to  perceive 
a  feeble  one.  It  is  sometimes  impossible  to  hear  the  sound 
of  a  human  voice  amid  a  heavy  storm ;  but  the  sound  of 
that  voice  exists.  At  the  same  time  it  is  equally  true  that 
feeble  sounds,  no  one  of  which  has  sufficient  energy  to 
awaken  sensation,  may  accumulate  upon  each  other,  unite 
their  forces,  so  to  speak,  and  thus  produce  a  confused 
sound,  which  commands  the  action  of  the  auditory  nerve ; 
e.  g.,  the  rustling  of  leaves,  or  "  the  hum  of  a  whispering 
school."  Tuning-forks  (or  diapasons)  like  those  men- 
tioned in  Exp.  5  require  great  care,  as  a  little  rust  or  a 
slight  change  in  the  elasticity  of  either  one  will  change  its 
rate  of  vibration.  In  such  case,  they  must  be  tuned  to 
unison  again  by  an  expert. 

After  using  the  forks,  wipe  them  with  a  woollen  cloth 
moistened  slightly  with  vaseline,  wrap  in  woollen  and  lay 
away  carefully.     See  Hand-Book  note  on  §  722. 

§  510.  The  following  beautiful  experiment  is  due  to 
Wheatstone :  Stand  a  long  wooden  rod,  an  inch  square, 
upon  a  music-box  or  the  sounding-board  of  a  piano.  Let 
it  pass  freely  through  two  ceilings  above.  In  the  second 
room  above,  on  the  end  of  the  rod,  place  a  violin.  When 
the  piano  is  played,  the  tremors  are  transmitted  through 
the  length  of  the  rod  to  the  violin  and  there  become 
plainly  audible  throughout  the  room,  although  in  the 
room  below,  between  the  piano  and  the  violin,  no  sound  is 
audible.     See  Daniell's  "  Principles  of  Physics,"  p.  379. 


[Element*  of  Natural  Philosophy,  pp.  393^397.]         197 

Exp.  S. — For  a  rope  •.'••  !t.  lung,  a  thickness  of  \  inch  is 
enough.  If  an  old  rope  can  not  be  liad,  the  new  one 
should  be  rolled  up  and  beaten  with  a  wooden  mallet  until 
it  is  quite  x't't. 

Exp.  10. — The  length  of  the  air-column  must  be  one- 
fourth  the  wave-length  because  the  pulse  started  by  the 
outward  swing  of  the  prong  of  the  fork  travels  twice  the 
length  of  the  air-column  in  half  a  wave-period  (§  482). 
We  know  this  from  the  reinforcement  of  sound  that  we 
hear.  When  the  pulse  has  travelled  the  length  of  the  air- 
column  twice,  it  coincides  with  the  effect  of  the  prong  as 
it  swings  in  the  opposite  direction.  If  the  pulse  travels 
twice  the  length  of  the  air-column  in  half  a  wave-period,  ft 
travels  once  that  length  in  a  fourth  of  a  wave-period.  This 
is  the  Baying  that  the  length  of  the  air-column  is 

one-fourth  the  wave-length. 

On  the  resonance  of  flames,  see  Harper's  Magazine  for 
March,  is: it.  p.  633.  Also  sec  Dolbear's  ••  The  Telephone," 
pp.  75-77. 


J  515.  The  accompanying  figure  represents  a  tube,  i, 
dividing  into  two  branches  at  c,  and  reuniting  at  c.  and 
thenoe  prolonged  to  o.  The  right-hand  branch  is  so  made 
that  the  part  b  n  may  slide  over  a  b.  When  b  is  pushed 
up  to  a,  the  two  branches,  cm  e  and  c  n  e,  are  of  equal 


108  [Elements  of  Natural  Philosophy,  pp.  395-405.] 

length.  If  a  sounding  tuning-fork  be  then  held  at  i  and 
the  ear  at  o,  the  sound  of  the  fork  is  distinctly  heard,  the 
waves  that  pass  around  by  //?,  and  those  that  pass  around 
by  n,  meeting  at  e  in  like  phases.  But  when  b  n  is  drawn 
out  (as  shown  in  the  figure)  to  a  certain  length,  determined 
by  trial,  the  sound  of  the  fork  is  wholly  destroyed.  This 
length  of  a  b  will  be  one-fourth  the  wave-length  of  the 
particular  fork  used,  for  then  the  path  of  the  waves  pass- 
ing by  n  is  half  a  wave-length  greater  than  the  path  of  the 
waves  passing  by  m.  The  waves  meet  at  e,  in  opposite 
phases,  and  a  total  interference  is  the  result.  The  parts 
of  the  tube  from  c  to  i  and  from  e  to  o  should  be  so  long 
that  the  sound  transmitted  directly  by  the  air  external  to 
the  tube  is  inaudible.  If  you  cannot  get  such  a  tube,  draw 
the  figure  on  the  black-board  and  explain  to  the  pupils 
what  it  means.  Ask  them  what  they  should  expect  when 
the  distance,  a  b,  equals  a  half  wave-length  and  in  what 
way  this  apparatus  may  be  used  to  determine  the  wave- 
length of  a  tuning-fork. 

§  519  (b).  See  Frick's  "Physical  Technics,"  p.  172 
(§  146).  Concerning  longitudinal  vibrations,  see  the  next 
paragraph  in  Frick. 

§  523.  See  Dolbear's  "  The  Telephone,"  p.  66.  Multi- 
plying by  11  the  numbers  in  the  last  line  of  §  521,  gives 
the  numbers  of  vibration  for  the  octave  when  C  has  264 
vibrations.     See  DanielPs  "  Principles  of  Physics,"  p.  387. 

For  description  of  methods  of  counting  vibrations,  see 
Deschanel's  "Natural  Philosophy,"  §§  651,  652. 

§  524.  Concerning  the  vibration  of  plates  and  nodal 
lines,  see  Deschanel's  "Natural  Philosophy,"  Fig.  565  and 
Mayer  on  "  Sound,"  Exps.  27-31. 

§  525.  See  Frick's  "Physical  Technics,"  p.  165  (§  136). 

§  529.  The  vibrations  of  the  strings  of  musical  instru- 
ments are  usually  compounded  of  several  of  these  modes 
of  vibration.  To  see  how  the  string  can  thus  vibrate  is 
not  easy ;  it  may  help  to  think  of  ripples  upon  the  waves 


[Fl>  phi/,  p.  JOS.]  109 

of  the  ocean.    The  Lower  tones  of  the  piano  contain  fptu 

or  live  harmonics  blended  with  the  fundamental,  while  in 
the  violin  there  are  still  more.  The  tuning-fork  is  probaU v 
as  free  from  harmonies  as  any  known  sonorous  body. 

Any  sound  may  be  resolved  into  a  combination  of  ele- 
mentary musical  tones  occurring  simultaneously  and  in 
>ueces8ion.      Hence,  the  study  of  musical   sounds   must 
necessarily  form   the  basis  of    acoustics.      See   DanielFs 
•  Principles  of  Physics,"  pp.  381,  382,  395-397. 

For  a  description  of  Lissajous'  Experiment  and  Black- 
burn's pendulum,  see  DcschaneFs  "Natural  Philosophy," 
76,  f577,  A.    Also  see  Mayer  on   "Sound,"  chapters 
1 V  and  XVII.     Concerning  manometric  flames,  see  Desch- 
aitel'fl  "  Natural  Philosophy,"  §  674. 

J5  530.  "  A  wooden  rod,  when  held  in  the  middle,  and  rubbed  half 
way  between  the  middle  and  one  end  with  chamois  leather  covered 
with  powdered  rosin,  emits  a  musical  note  due  to  longitudinal  vibra- 
tion of  the  rod.  The  rod,  in  fact,  alternately  stretches  and  contracts, 
the  middle  remaining  stationary,  while  the  two  ends  recede  from  it 
together  and  approach  it  together.  The  cross  section  at  the  middle 
is,  therefore,  a  node  and  the  ends  are  autinodes. 

"  The  time  of  a  complete  vibration  is,  just  as  in  the  case  of  u 
string  or  an  open  organ  pipe,  the  time  that  a  pulse  would  occupy 
in  traveling  over  twice  tin*  length  of  tin-  rod.  Hence,  from  observing 
the  pitch  of  the  note  emitted,  the  velocity  with  which  longitudinal 
pulses  travel  along  the  rod  can  be  inferred.  For  example,  if  the 
npte  be  Cof  512  vibrations  persecondandthe  length  of  the  rod  be  10 
feet, a  length  of  20  feet  is  travelled  over  512  times  in  a  second  and 
the  velocity  is  10,240  feet  per  second.  This  is  one  of  the  most  con- 
\.  ii.  nt  practical  methods  of  determining  the  velocity  of  sound  in 
solid  bodies. 

'  The  existence  of  nodes  in  a  vibrating  body  is  beautifully  shown 
by  firmly  fixing  a  square  plate  of  metal  in  the  middle  and  bowing  the 
with  a  well  rosined  double  bass  or  violoncello  bow.  By  varying 
the  bowing,  the  plate  can  be  made  to  give  several  distinct  no:, 
if  sand  be  sifted  over  the  plate,  it  quickly  settles  on  the  nodal  lines 
in  each  case.  For  the  deepest  tone,  the  nodal  lines  divide  the  plate 
into  four  equal  squares.  For  the  next  tone,  they  divide  it  into  four 
equal  triangles.  For  some  of  the  higher  tones,  they  form  very  elabo- 
rate figures.     To  obtain  any  particular  figure  known  to  be  among 


200  [Elements  of  Natural  Philosophy,  pp.  405,  406.] 


those  which  the  plate  is  capable  of  giving,  the  finger  should  be 
applied  to  one  of  the  nodal  lines  of  that  figure  and  the  bow  should 
be  applied  about  midway  between  two  nodal  lines." — Everett. 

If  very  light  powder 
(e.  g.,  lycopodium)  be 
mixed  with  the  sand, 
it  will  not  move  with 
the  sand  to  the  nodal 
lines  but  will  form  little 
heaps  in  the  centres  of 
the  vibrating  segments. 
These  heaps  will  be  in 
a  state  of  violent  agita~ 
tion  with  more  or  less 
of  gyratory  movement 
as  long  as  the  plate  is  vibrating.  These  motions  are  due 
to  currents  of  air  caused  by  the  vibrations  of  the  plate.  In 
a  vacuum,  the  powder  will  go,  with  the  sand,  to  the  nodal 
lines. 

The  writing  sand  and  sifting  boxes  sold  by  stationers  are 
desirable  for  the  above  experiment  with  Chladni's  plate. 

§  533.  Let  one  side  of  an  open  organ  pipe  be  made  of 
glass.  Stretch  a  membrane  on  a 
frame  small  enough  to  enter  the 
pipe.  Sprinkle  some  sand  on  the 
membrane  and  lower  it  into  the 
pipe.  The  sand  grains  will  exe- 
cute a  lively  dance  with  enough 
noise  to  be  easily  heard. 

When  a  tube,  open  at  both 
ends,  is  held  so  as  to  surround 
a  small  hydrogen  flame  (see  Ele- 
ments of  Chemistry,  §  21)  a  musi- 
cal tone  is  heard,  which  varies 
with  the  dimensions  of  the  tube 
and  often   attains    considerable 


[EUments  of  Katural  Philosophy,  pp.  4O6-4W.]         201 

power.  The  sound  is  due  to  the  vibration  of  the  air  and 
products  of  combustion  within  the  open  pipe.  The  vibra- 
tion is  caused  l»v  alternate  rising  and  falling  of  the  flame. 
See  Elements  of  Chemistry,  Exp.  29. 

§  535,  a.  See  Daniell's  "  Principles  of  Physics,"  p.  440. 


Note. — Concerning  harmony  and  dissonance,  see  Darnell's  "Prin- 
ciples of  Physics,"  p.  437. 


Exercises,  Page  408, 

1.  144  x  {  =  180,  the  number  of  vibrations  for  its 
third.     (§  521.) 

144  x  f  =  216,  the  number  of  vibrations  for  its  fifth. 
144  x  2  =  288,    '•        "         "        "  "   "  octave. 

2.  Wave  length =(1,120  ft.  -h  512=)  2.1875  ft.  (§  482.) 
2.1875  ft.  -^  2  =  1.09375  ft.     (§  533.)— Am. 

3.  See  §  519,  (1.).  (a.)  50  vibrations,  (b.)  200  vibra- 
tions. 

4.  i  of  i  of  100  =  25.— Ans. 

5.  Ignore  the  number  of  vibrations  and  see  §  519. 

G.  (a.)  17£ft.     (b.)  ljin.     (See  second  problem  above.) 

7.  (a.)  2  ft.     (b.)  1  ft. 

8.  (a.)  5  ft.  (b.)  1,120  ft,  ^  5  ft.  =  224,  the  number 
of  waves  started  each  second.  The  period  of  each  wave 
is  ¥£j  of  a  second. 

9.  Three  beats  per  second. 

10.  (b.)  398  or  402  per  second. 

11.  320;  384;  512. 

li.   264  x  2  x  i  =  792. 

L'rciric  fjtfcstions,  Page  410, 

5.  (d.)  See  §  523.  If  the  instrument  be  tuned  to  the 
pitch  adopted  by  the  English  we  shall  have  204  x  2  x  j 
=  880.—  .! 


202  [Elements  of  Natural  Philosophy,  pp.  4 10,  411.) 

8.  (a.)   v  =  144.72  ft.;    2  x  144.72  %  289.44.— ^«& 

40002 
(&)  20  lb.  x  ^*  =  20  lb.    x   «  =  20  lb.    x   |  = 

8|  lb.— ^rcs. 

10.  (a.)  See  Fig.  116.  The  atmospheric  pressure  at  B 
would  equal  that  at  A  or  at  C.  Gravity  would  draw  the 
water  in  the  long  arm  down  to  C,_  and  that  in  the  short 
arm  down  to  A.  The  action  of  the  siphon  would  be  de- 
stroyed, (b.)  The  height  to  which  the  water  could  be  raised 
(a  b  in  Fig.  116)  would  be  lessened  because  of  the  diminu- 
tion in  atmospheric  pressure,  (c.)  The  liquid  would  rise 
through  the  atmosphere  except  what  could  be  retained  in 
the  siphon  above  the  level  of  the  lower  end  of  the  shorter 
arm. 

15.  Strike  a  key  of  a  piano ;  strike  it  again  with  more 
i>rce.  The  tones  differ  in  intensity.  Strike  a  key  of  a 
piano;  strike  another  key  with  equal  force.  The  tones 
differ  in  pitch.  Strike  a  key  of  a  piano ;  sound  the  same 
tone  with  equal  loudness  upon  a  flute.  The  tones  differ 
in  timbre. 

18.  v  =  8.02  Vh.  The  velocity  of  the  jet  is  56.14  ft.  or 
673.68  in.  The  quantity  of  water  discharged  per  second 
is  1347.36  cu.  in.  The  quantity  of  water  discharged  in 
3600  seconds  is  4850496  cu.  in.,  or  20997  gal.  189  cu.  in  — 

Ans. 

23.  (a.)  During  the  6  seconds  it  falls         578.88  ft. 
"        "  first  4  seconds  it  falls  257.28  ft. 


<M 


(c.)  See  §  72(3)  and  §  93. 
24.  (a.)  Suppose  the  weights  to  be  5  oz.  and  3  oz.  respec- 


a 

a 

last  2 

a 

a 

a 

321.6    ft— 

Ans, 

tc 

a 

4.1 

a 

n 

a 

270.3048  ft. 

u 

it 

first  4 

a 

a 

a 

257.28      ft. 

a 

a 

last  tV 

a 

a 

a 

13.0248  ft. 
Ans. 

[Elements  of  Natural  Philosophy,  pp.  410-411.]  203 

tively.  We  then  have  a  force  of  2  oz.  to  move  a  weight  of 
8  oz.  If  the  weights  were  falling  freely,  we  should  have 
a  force  of  8  oz.  to  do  the  same  work.  The  force  of  2  oz. 
can  do  the  work  only  \  as  rapidly  as  a  force  of  8  oz.  on  Id 
doit     See  §  67  and  §  70  (a). 

(b.)  Suppose  the  weights  to  be  7pwt.  and  5  pwt.  respect- 
ively. We  have  now  a  force  of  2  pwt.  to  move  a  weight 
of  12  pwt.  If  the  weights  were  falling  freely,  the  force  of 
12  pwt.  would  give  to  the  weights  of  12  pwt.  an  increment 
of  velocity  =  g,  or  32.16  ft.,  or  9.8  m.  (§  127.)  As  our 
force  of  2  pwt.  is  only  }  of  the  force  necessary  to  produce 
this  effect,  the  result  will  be  only  £  as  great,  or  the  incre- 
ment will  be  \  g. 

25.  The  resistances  in  the  circuit  are  2,040  ohms  -f  2,850 
ohms  +  250  ohms  -f-  574  ohms  =  5,714  ohms.  Tha 
E.  M.  F.  of  the  battery  is  40  volts  (§  399,  a). 

See  §  386.     C  =  ^-  =  ~^  =  0.007,  the  number  of 

amperes.     But  0.007  amperes  =  7  milliamperes. 

26.  The  electroscope  was  first  polarized  (§  332)  and  then 
charged  by  induction  (§  334).  Suppose  that  the  charge  of 
the  electrified  body  being  tested  is  —  ;  then  the  charge  of 
the  gold  leaves  is  -f.  Bringing  a  positively  charged  body 
near  the  electroscope,  will  add  to  the  +  electricity  of  the 
It  ;i\es  by  further  polarization,  attracting  more  of  the  — 
electricity  to  the  knob  (§  337  [2"|).     The  +  charge  of  the 

<  being  thus  increased,  the  leaves  will  diverge  more 
widely.  If  the  original  charge  be  +,  instead  of  — ,  as 
herein  assumed,  the  electroscope  will  be  negatively  charged 
by  induction  and  the  approach  of  a  second  body  positively 
charged  will,  by  polarization,  lessen  the  excess  of  —  elec- 
tricity in  the  leaves  by  repelling  +  electricity  thither  and 
thus  diminishing  their  mutual  repulsion. 

27.  (a.)  C  =   p   =rjs  10,  the  number  of  amperes, 

1\  0.0 


204  [Elements  of  Natural  Philosophy,  p.  4. 11.] 

(b.)  See  §  471.     H  =  C*Rt  x  0.24  .=  100  x  3.6  x  1  x 
0.24  =  86.4. 

,S.  (a.)   0  =  §  =  ^— L  =  0.144. 

(*.)  H=  C2fitx  0.24=0.020736x46.64x600x0.24= 
139.266,  the  number  of  lesser  calories. 

Consulting  the  index,  concerning  "lesser  calorie,"  we 
are  referred  to  §  579,  where  we  learn  that  one  such  unit 
will  warm  one  gram  of  water  one  degree  centigrade.  Con- 
sequently, 139,266  such  units  will  warm  100  grams  of 
water  (ice  cold,  or  at  0°  C.)  as  many  centigrade  degrees  as 
100  is  contained  times  in  139.266,  or  1.39266  degrees. 


CHAPTER  VIII 

§  537.  See  First  Prin.  Nat.  Phil,  Exps.  168-171  and 
§§  355,  356. 

I  iS.  M  Up  to  the  middle  of  the  present  century,  heat,  electricity, 
magnetism,  etc.,  were  supposed  to  be  material  substances  whose  in- 
terconvertibility  with  mechanical  motion  or  energy  appeared  to  be 
utterly  inconceivable.  It  was  only  after  the  establishment  of  the 
dynamic  theories  of  the  *  imponderables '  that  the  doctrine  of  the 
conservation  and  transformation  of  energy  became  fertile  and  led  to 
a  fundamental  reconstitution  of  the  entire  body  of  physics."— Stallo. 

It  might  be  more  accurate  to  say  that  we  use  the  word 
heat  to  designate  two  forms  of  energy.  One  of  these  is 
the  energy  of  an  ether  wave  (§§  608,  610)  and  is  called 
radiant  heat.  The  other  form  is  that  of  "a  confused, 
oscillatory  disturbance  of  the  particles  of  a  body  "  and  "  i^ 
the  only  form  of  heat  for  which  we  have  special  sense- 
organs.  We  do  not  directly  perceive  the  undulations  o. 
radiant  heat  by  our  senses ;  when  the  sun  shines  on  us, 
heat  waves  strike  the  skin  and  throw  it  into  vibrations. 
This  sensible  heat  of  the  skin,  not  the  radiant  heat  of 
space,  affects  the  appropriate  nerve-ends."  This  second 
form  of  heat  energy  is  what  we  are  first  to  consider. 

u  Heat  is  the  lowest  form  of  energy.  It  may  be  said  to  have  no 
organization  but  to  depend  on  undirected  and  blind  activity  of  mole- 
cules, which  dash  hither  and  thither.  When,  in  any  action,  energy 
is  liberated  which  is  not  guided  by  the  environment  into  any  special- 
ized form,  it  manifests  itself  as  heat;  and  when  energy  is  spent  in 
doing  work,  the  equivalent  of  which  appears  in  no  other  form,  it 
thth  ,//,p,,irn  as  heal.  This  statement  is  widely  applicable  and  im- 
portant."— Daniell. 


206  {Elements  of  Natural  Philosophy,  pp.  ^12,  413.] 

The  imaginary  material  substance  that  was  supposed  to 
be  the  cause  of  thermal  phenomena  was  called  caloric. 
The  idea,  caloric,  is  no  longer  entertained,  but  the  word 
still  lives  in  its  derivatives,  calorific,  calorimeter,  etc.  Ca- 
loric was  supposed  to  pass  from  one  body  to  another, 
changing  temperatures  and  producing  liquefaction  or  solidi- 
fication, vaporization  or  condensation.  But  the  substance 
could  never  be  detected  by  the  most  delicate  balances. 
Near  the  close  of  the  last  century,  some  remarkable  experi- 
ments were  made  by  Count  Rumford.  They  should  have 
resulted  in  the  immediate  annihilation  of  the  idea  of 
caioric.  As  a  result  of  his  observations  while  engaged  in 
superintending  the  boring  of  cannon  at  Munich,  he  actually 
boiled  water  by  heat  developed  by  the  friction  of  a  blunt 
boring  tool  pressed  against  the  bottom  of  a  hollow,  iron 
cylinder  and  turned  by  horse-power.  See  Tyndall's  "  Heac, 
a  Mode  of  Motion,"  Appendix  to  Chapter  2.  It  was  evi- 
dent that  this  heat  could  not  have  come  from  any  of  the 
bodies  present ;  also  that  heat  would  be  evolved  as  long  as 
the  friction  was  continued.  Rumford  was  an  American  by 
oirth  and  early  education,  being  known,  while  in  this  coun- 
try, as  Benjamin  Thompson.  Read  the  sketch  of  his  life 
in  some  biographical  dictionary  or  cyclopaedia. 

Early  in  this  century,  Sir  Humphrey  Davy  (Royal  Insti- 
tution, London)  melted  ice  by  the  friction  of  one  piece 
upon  another,  in  a  vacuum,  in  a  room  with  a  tempera- 
ture below  the  melting  point  of  ice,  0°  C.  There  was  no 
available  source  of  "caloric";  the  heat  was  generated  by 
friction ;  it  was  a  form  of  motion.  Tait's  "  Heat,"  pp. 
21-32. 

§  539.  The  temperature  of  a  body  depends  on  the  veloc- 
ity of  agitation  of  the  molecules  of  that  body.  See  First 
Prin.  Nat.  Phil,  §  358  and  Tait's  "  Heat,"  pp.  1-7. 

§  541.  For  a  description  of  the  various  kinds  of  ther- 
mometers and  their  use-,,  see  the  "  Scien  tific  American  Sup 
plement,"  No.  59,  and  Frick's  "  Physical  Technics,"  pp.  405 
to  412.   The  most  delicate  instrument  for  the  measurement 


ol  beal  is  Edison's  iasimetet,  concerning  which*  Bee  the 
•'  Scientific  American/'  vol.  3s,  p.  :J85. 

If  we  were  quite  sure  of  the  bulk  measurement  given  by  the  glass 
bulb  and  tube,  liquid  thermometers  would  be  quite  u  MXUU9 
gas  thermometers.  But,  alas  for  thermometry,  the  glass  measure 
is  not  constant !  It  is  found  that  the  bulb  of  a  thermometer  is  pot 
always  of  the  same  volume  »t  the  same  temperature,  but  that  it  ex 
perienees  uncertain  changes  exceedingly  embarrassing.  In  the 
course  of  a  few  monthfl  alter  a  thermometer  is  filled  and  sealed,  the 

bulb  generally  shrinks  by  some  uncertain  amount  (ft"001  40000  to 
10  000  °'  lta  bulk).  This  has  been  discovered  by  a  gradual  rising  of 
the  freezing  point,  in  new  mercury  thermometers,  as  much  as  0.35° 
to  1    C,     After  a  few  months  or  years,  this  progressive  shrinkage 

to  be  sensible.  But  if  the  thermometer,  at  any  time,  be  ex- 
posed to  the  temi>erature  of  boiling  water  or  any  higher  temperature, 
an  abrupt  subpermanent  enlargement  of  the  bulb  is  produced  and 
the  freezing  point  is  found  to  be  lowered.  Then  again,  for  weeks 
And  months  and  years,  there  is  a  gradual  shrinkage  as  shown  by  a 
gradml  rising  of  the  freezing  point  (?  543).  A  very  delicate  mer- 
:  ury  thermometer  that  has  been  kept  for  years  at  ordinary  atmos- 
pheric pressures  when  out  of  use  and  never,  when  in  experimental 

\ posed  to  any  temperature  higher  than  30°  C  or  much  lower 
than  0  C.  becomes  very  constant  and  may  not  show  any  change  of 
as  much  as  0.1°  C.  within  the  rang'  from  —  20'  C.  to  40°  C.  But 
the  abrupt  and  irregular  changes  produced  by  exposing  the  ther- 
mometer to  temperatures  much  above  or  much  below  some  such 
limited  range  as  that,  constitute  a  very  serious  difficulty  in  the  way 

urate  thermometry  by  the  mercury-in-glass  thermometer. 
cJee  M  Encyclopaedia  Britannica,"  §  19  of  Article  "  Heat." 

I-'..r  HiiijM  raimvs  below  the  freezing  point  of  mercury 
(—  89.4°  C),  alcohol  thermometers  are  generally  need. 
Per  v. tv  high  temperatures,  pyrometers  and  other  instru- 
ments are  used.  One  form  of  pyrometer  ia  described  on 
the  ii'  Thermometers  used  to  register  the  hL 

or  the  lowest  temperature  within  a  given  period  are  called 
registering  thermometers.    They  are  of  two  classes. 

If  the  tube  of  amerury  thermometer  be  sufficiently  eouirarted  just 
the  bulb  and  the  tube  pined  In  i  horizontal  position,  mercury 


208  {Elements  of  Natural  Philosophy,  pp.  J/.13,  417.] 

will  be  pushed  through  the  neck  when  the  temperature  rises  and  fails 
to  return  when  the  temperature  subsequently  falls.  The  mercury 
thus  left  in  the  tube  serves  as  an  index  to  show  the  highest  tempera- 
ture reached  during  the  time  of  exposure.  Such  an  instrument  is 
-palled  a  maximum  tliermometer.  It  is  readjusted  for  a  subsequent 
observation  by  bringing  it  into  a  vertical  position. 

Alcohol  is  used  in  the  minimum  thermometer.  The  horizontal 
tube  contains  an  index  of  glass  which  is  of  less  diameter  than  the 
bore  of  the  tube.  The  instrument  is  adjusted  for  use  by  bringing 
the  index  into  contact  with  the  end  of  the  alcohol  column  in  the  tube. 
When  the  alcohol  expands,  part  of  it  flows  by  the  index  without 
moving  it.  When  the  temperature  falls,  the  index  adheres  to  the 
end  of  the  receding  alcohol  column  and  is  drawn  after  it  into  a  posi- 
tion that  indicates  the  minimum  temperature  reached  during  the 
period  of  exposure. 

See  Deschanel's  "Natural  Philosophy,"  §§  178-193. 

§  548.  The  increase  in  length  of  a  linear  unit  of  a  solid 
body  when  it  is  heated  from  0°  C.  to  1°  C,  is  called  the  co- 
efficient of  linear  expansion  for  that  substance.  For  homo- 
geneous solids,  the  coefficient  of  voluminal  expansion  is 
three  times  the  coefficient  of  linear  expansion. 

The  expansion  of  a  liquid  may  be  absolute  (i.  e. ,  its  real  increase 
in  volume)  or  apparent  (i.  e.,  its  increase  in  volume  relative  to  the 
increase  in  the  capacity  of  the  containing  vessel).  For  example,  the 
absolute  expansion  of  mercury  in  a  thermometer  is  greater  than  its 
apparent  expansion.  The  determination  of  the  coefficient  of  expan- 
sion of  mercury  is  of  great  importance  because  this  liquid  is  used 
for  so  many  purposes  in  scientific  investigation,  bee  Deschanel's 
"  Natural  Philosophy,"  §§  177  (2) ;  194-201. 

§  549.  Linear  expansion  may  be  shown  by  the  pyrometer, 
an  instrument  represented  in  the  figure.  One  end  of  the 
metallic  rod,  A,  is  fastened  at  B,  while  the  other  end 
passes  freely  through  the  post,  C,  and  presses  against  the 
short  arm  of  the  lever,  P.  The  long  arm  of  the  lever 
forms  a  pointer  which,  by  moving  over  the  graduated  arc, 
renders  visible  any  change  in  the  length  of  A.  The  rate 
of  expansion  for  the  rod  being  known,  the  pyrometer  may 
be  used  (as  its  name  indicate*)  to  measure  temperatures. 


[Elements  of  Natural  Philosophy,  pp.  417,  41$.']  209 

See  First  Prin.  Nat.  Phil.,  Exp.   173;    "Nature,"  Vol. 
35,  p.  89;  Deschancl's  "Natural  Philosophy,"  §§  202-205. 

§  550.  The  experiment  with  the  brass  and  iron  bar  may 
be  represented  by  placing  a  thin  card  of  gelatine  on  tbe 


palm  of  the  hand.  The  gelatine  being  a  poor  conductor; 
the  under  surface  becomes  the  warmer  and  expands  the 
more,  thus  bending  the  edges  upward.  When  thick  glass- 
ware is  strongly  heated,  it  tends  to  bend  in  a  similar  way, 
but  as  it  has  little  flexibility,  the  tendency  often  results  in 
breakage. 

(a.)  The  now  common  incandescence  electric  lamps  may 
be  used  for  the  illustration  of  this  fact. 

§  552.  See  Frick's  "  Physical  Technics,"  p.  413  (§  347) 
and  Deschanel's  "Natural  Philosophy,"  §§  206-216. 

*  When  heat  is  applied  to  a  body,  it  increases  the  kinetic  energy 
of  the  molecules  (raises  the  temperature),  and  increases  the  potential 
energy  by  forcing  the  molecules  further  apart  against  their  mutual 
attractions  and  any  external  forces  that  may  resist  expansion.  Since 
the  internal  work  to  be  done  when  a  solid  or  liquid  expands  varies 
greatly  for  different  substances,  it  would  be  expected  that  the 
amount  Of  »*xpansion  for  a  given  rise  of  temperature  would  vary 
greatly."— Anthony  and  Brackett. 


210  [Elements  of  Natural  Philosophy,  pp.  420,  421.] 

§  555.  See  First  Prin.  Nat.  Phil,  Exps.  174,  176 ;  also 
Deschanel's  "Natural  Philosophy,"  §§  177  (3) ;  217-224. 

§  557.  "  If  air  be  substituted  for  mercury  in  the  thermometer  and 
means  provided  for  maintaining  its  volume  constant  and  measuring- 
its  pressure,  the  instrument  becomes  an  air  thermometer.  The  air 
thermometer  is  taken  as  the  standard  instrument  for  scientific  pur- 
poses. Its  use,  however,  involves  several  careful  observations  and 
tedious  computations.  It  is,  therefore,  mainly  employed  as  an  in- 
strument with  which  to  compare  other  instruments.  By  making 
such  a  comparison  and  constructing  a  table  of  corrections,  the  read* 
mgs  of  any  thermometer  may  be  reduced  to  the  corresponding  read- 
ings of  the  air  thermometer." — Anthony  and  Brackett. 

§  558.  When  we  double  the  kinetic  molecular  energy  of 
a  body  we  double  its  absolute  temperature. 


[Elements  of  Natural  Philosophy.]  211 

Eocercise*,  Page  423. 

1.  273  :  273  +  30  =  900  :  x ;    .-.  x  =  998.9. 

2.  273  +  10  :  273  =  170  :  x ;    .\  x  =  164—. 

3.  273  :  373  =  1,000  :  x ;    .\  x  =  1,366.3. 

4.  288  :  323  =  x  :  15,000  ;    .-.  x  —  13,374.6. 

5.  185°  F.  =  85°  C.     (§546.) 

358  :  283  =  98  :  x ;     .-.  x  =  77.4  +  . 

6.  (§  557.)     490  :  500  =  1,000  :  x  ;    .:  x  =  980. 

7.  283:291.7)        __  ,  ..  _  , 
590:530     [  =  lo5  :  *  ;     •'****«■•»** 

8.  273  :  333  =  231  :  z;  .-.  a:  =  281.7  +  . 

°.  The  20  cu.  ft.  or  34,560  cu.  in.  of  air  weighs  10,713.6 

grams.      (§272.)     _+_=_  =  -.    The  balloon 

full  of  heated  air  will  weigh  |f  °f  10,713.6  gr.;  the  weight 
thus  supported  will  be  Jf  of  10,713.6  gr.  =  1,847-1-  gr. 

10.  f  of  36  =  20.     Ans.,  20°  C. 

11.  |  of  35  =  63.     Aiut.,  63°  F. 

12.  (a.)  20°  C.    (b.)  68°  F. 
273  +  30        1,109,890 


13. 


273        ~~  1,000,000 


1  .    373  x  1,013,600        1,385 

14  ^73-x-Tooo^oo  =  i^oo  • the  number  of  llters- 


212  [Elements  of  Natural  Philosophy,  p.  4££.] 

§  560.  The  effects  of  an  increase  of  heat  in  a  body  are 
partly  internal  work  and  partly  external  work.  The 
internal  ivork  may  be  to  increase  the  kinetic  energy  of  the 
molecules,  i.  e.,  to  raise  the  temperature ;  to  work  a  change 
of  volume,  cohesion,  elasticity,  etc.,  such  work  being  dono 
by  or  against  the  molecular  forces ;  to  produce  vibrations 
within  the  several  molecules ;  and  to  work  chemical 
changes.  The  external  work  is  done  by  or  on  a  body  as  it 
expands  or  shrinks. 

Suppose  an  iron  bar  to  be  heated  in  a  vacuum.  The 
work  done  by  the  heat  is  two-fold ;  an  increase  of  tempera- 
ture and  expansion.  The  expansion  represents  work  done 
against  the  molecular  forces.  When  the  same  bar  is  heated 
in  the  air,  the  work  done  is  three-fold.  The  two  kinds  oi 
internal  work  done  in  the  former  case  are  repeated  and 
external  work  is  added,  for  the  surrounding  atmosphere  is 
pushed  back  by  the  expanding  iron.  In  this  case,  the 
external  work  is  relatively  very  small. 

Suppose  a  given  quantity  of  a  gas  to  be  heated.  Very 
little  work  is  done  against  the  molecular  forces  in  expand- 
ing the  gas  (§§  57,  62),  the  work  done  being  chiefly  two- 
fold, namely,  the  internal  work  of  raising  the  temperature 
and  the  external  work  of.  overcoming  the  atmospheric  (or 
other)  pressure. 

Suppose  water  above  the  temperature  of  4°  C.  to  be 
heated.  It  expands  (§  553).  The  work  done  by  the  heat  is 
three-fold,  namely,  the  internal  work  of  raising  the  tem- 
perature and  separating  the  molecules  to  a  greater  dis- 
tance from  each  other  (expansion)  and  the  small  amount 
of  external  work  involved  in  pushing  back  the  atmosphere. 

Now  suppose  that  water  at  0°  0.  is  heated  to  3°  C.  It 
contracts.  The  heat  works  an  elevation  of  temperature ; 
internal  work  is  done  by  the  molecular  forces  in  crowding 
the  molecules  nearer  together.  External  work  is  also  done 
by  the  atmospheric  pressure. 

In  the  process  of  liquefaction,  nearly  all  of  the  work  is 


[Elements  of  Natural  Philosophy,  pp.  424-426.]  213 

internal  and  ia  spent  in  producing  ■  new  arrangement  of 
the  molecules.  If  expansion  accompanies  the  liqoeiaction 
(as  is  usually  the  case),  externa]  wmk  i>  done  and  addi- 
tional heat  is  needed.    If  contraction  is  the  accompaniment 

(as  in  the  case  of  melting  ice),  external  work  is  done  by 
the  atmospheric  pressure  and  less  heat  energy  is  needed. 

This  indicates  that  the  freezing  point  of  water  is  low 
by  pressure. 

§  5C2.  Some  substances,  when  heated,  decompose  1»< 
melting.  Under  certain  conditions,  a  liquid  may  be  cooled 
below  the  melting  point  without  solidifying  (§  588).  Some 
alloys  melt  at  a  lower  temperature  than  any  of  their  con- 
stituents ;  e.g.,  an  alloy  of  tin.  had.  bismuth  and  cadmium 
melts  at  62°  C. 

M.  "  There  are  many  reasons  for  believing  that  the  molecules 
of  solids  and  liquids  are  in  a  state  of  continual  motion.  It  can  easily 
be  supposed,  that,  at  the  "exposed  surface  of  the  substance,  the 
motion  of  a  molecule  may  at  times  be  so  violent  as  to  project  it  be- 
yond the  reach  of  the  mutual  attractions.  If  this  occur  in  the  air 
or  in  a  space  filled  with  any  gas,  the  molecule  may  bo  turned  back 
and  made  to  rejoin  the  molecules  in  the  liquid  mass  ;  but  many  will 
find  their  way  to  such  a  distance  that  they  will  not  return.  They 
then  constitute  a  vapor  of  the  substance.  As  the  number  of  free 
molecules  in  the  space  above  tin-  liquid  increases,  it  is  plain  that 
then  may  come  ■  time  when  as  many  will  rejoin  the  liquid  asescape 
from  it.  The  space  is  then  saturated  with  the  vapor.  The  more 
violent  the  motion  in  the  Liquid,  i.  6.,  the  higher  its  temperature,  the 
more  rapidly  will  the  molecules  escape,  and  the  greater  must  be  the 
Dumber  la  the  space  above  the  liquid  before  the  returning  will  equal 
the  outgoing  molecules.  In  other  words,  the  higher  the  tem|>craturp, 
the  mon-  dene  •  the  vapor  that  saturates  ■  given  space.  If  the  space 
above  a  liquid  be  a  vacuum,  the  escaping  molecules  will  at  first  meet 
with  no  obstruction  and,  as  a  consequence,  the  space  will  lx-  very 
quickly  saturated  with  the  vapor." — Anthony  <n,d  Bmckttt. 

"  If  any  of  the  molecules  at  the  surface  of  the  liquid  have  puch 
velocities  (equal  to  or  greater  than  the  average  velocity  in  the  vjipor1 
and  if  they  are  moving  from  the  liquid,  they  will  escape  from  those 
which  retain  the  other  molecules  as  constituents  of  the  liquid 
and  will  fly  about  as  vapor  in  the  space  outside  the  liquid.  This  is 
the  molecular  theory  of  evaporation, 


214  [Elements  of  Natural  Philosophy,  pp.  426-429.] 

'  At  the  same  time,  a  molecule  of  the  vapor  striking  the  liquid 
may  become  entangled  among  the  molecules  of  the  liquid  and  thus 
become  part  of  the  liquid.  This  is  the  molecular  explanation  oi 
condensation. 

"  The  number  of  molecules  that  pass  from  the  liquid  to  the  vapor 
depends  on  the  temperature  of  the  liquid.  The  number  of  molecules 
that  pass  from  the  vapor  to  the  liquid  depends  upon  the  density  of 
the  vapor  as  well  as  its  temperature.  If  the  temperature  of  the 
vapor  is  the  same  as  that  of  the  liquid,  evaporation  will  take  place 
as  long  as  more  molecules  are  evaporated  than  are  condensed  ;  but 
when  the  density  of  the  vapor  has  increased  to  such  a  value  that  as 
many  molecules  are  condensed  as  are  evaporated,  then  the  vapor  has 
attained  its  maximum  density.  It  is  then  said  to  be  saturated  and 
it  is  commonly  supposed  that  evaporation  ceases.  According  to  the 
molecular  theory,  however,  evaporation  is  still  going  on  as  fast  as 
ever  ;  only  condensation  is  going  on  at  an  equal  rate,  since  the  pro- 
portions of  liquid  and  of  gas  remain  unchanged." — Maxwell. 

§  565.  ■  See  Frick's  "  Physical  Technics/'  p.  421,  Fig.  734. 

For  many  laboratory  experiments  where  an  intense  heat 
is  needed,  the  common  Bunsen  burner,  which  may  be 
obtained  of  any  dealer  in  philosophical  or  chemical  appara- 
tus, is  exceedingly  convenient.  But  this  requires  a  supply 
of  illuminating  gas,  with  which  not  every  school  labora- 
tory is  provided.  For  laboratories  not  provided  with  gas, 
the  author  recommends  Kellogg's  Vapor  Bunsen  Lamp. 
Either  of  these,  as  well  as  the  ordinary  alcohol  lamp  (see 
Fig.  295),  gives  much  heat  without  the  deposition  of  soot. 

§  567.  On  the  influence  of  vibratory  motion  upon  the 
boiling  point,  see  Harper's  Magazine,  for  March,  1879, 
p.  632. 

A  tray  may  be  made  of  a  sheet  of  writing  paper  by  turning  up  a 
strip  an  inch  wide  on  each  of  the  four  sides  of  the  sheet  and  pinning 
at  the  corners.  Such  a  tray  may  be  nearly  filled  with  water  and 
placed  on  a  hot  stove.  The  water  may  be  boiled  without  charring 
the  paper,  for  the  vaporization  of  the  liquid  keeps  the  temperature 
down  to  100°  C.  This  temperature  is  not  high  enough  to  destroy 
the  tray. 

§  569.  "  When  a  liquid  is  heated  in  a  limited  space,  the  vapor 
generated    accumulates,   increasing  the  pressure  and  causing  the 


[Element*  of  Natural  Philosophy,  pp.  4*9-4Jg.]  215 


tem]>erature  to  rise  above  the  ordinary  boiling  point.  Experiments 
upon  liquids  in  spaces  but  little  larger  than  their  own  volumes  show 
that,  at  a  certain  temperature,  the  liquid  suddenly  disappears  ;  thai 
is,  it  is  converted  into  vaj>or  in  a  space  but  little  larpr  th;m  it-  own 
volume.  It  is  supposed,  that  above  the  temperature  at  winch  this 
occurs,  which  is  called  the  critical  temperature,  the  substance  cannot 
exist  in  the  liquid  state." — Anthony  and  Brackett. 

§  570.  The  same  principle  may  be  illustrated  by  the  ap- 
paratus represented  in  the  accompanying  figure.  The 
receiver,  R,  having 
been  exhausted  with 
an  air-pump,  is 
closed  by  the  stop- 
cock, ft.  The  flask, 
F9  is  half  full  of  water 
and  heated  by  a  lamp 
placed  beneath. 

As  the  water  boils, 
tin-  steam  escapes 
through  the  open 
stop-cocks,  a  and  c. 
When  the  steam  has 
i  \pelled  the  air  from 
/■'.  (lose  a  and  c,  removing  the  lamp  at  the  same  time. 
The  water  gradually  cools  and  ceases  to  boil.  Water  may 
be  dashed  over  Fmd  the  water  made  to  boil  as  in  the  last 
experiment.  When  this  has  been  done  a  few  times,  the 
water  may  be  allowed  to  come  to  rest.  It  will  be  several 
degrees  below  the  boiling  point.  Opening  a  and  ft,  the 
\apor  of  F  escapes  into  R  and  the  water  begins  to  boil 
vigorously.  By  keeping  R  cool,  the  water  in  ^Fmay  be 
made  to  boil  for  a  considerable  time. 

§  573.  "  If  a  liquid  be  introduced  into  a  highly  heated  capsule,  of 
poured  upon  a  very  hot  plate,  it  does  not  wet  the  heated  surface,  but 
forms  a  flattened  spheroid,  which  presents  no  appearance  of  boiling 
hut  i-vaporates  very  slowly.  The  temperature  of  the  spheroid  is 
below  the  boiling  point  of  the  liquid.    The  spheroid  does  not  touch 


216  [Elements  of  Natural  Philosophy,  p.  432.] 

the  heated  plate  but  is  separated  from  it  by  a  non-conducting  layer 
of  vapor.  This  accounts  for  the  slowness  of  the  evaporation.  To 
maintain  the  spheroid,  the  temperature  of  the  capsule  must  be  much 
above  the  boiling  point  of  the  liquid  ;  for  water,  it  must  be  at  least 
200°  C.  If  the  capsule  be  allowed  to  cool,  the  temperature  will  soon 
fall  below  the  limit  necessary  to  maintain  the  spheroid,  the  liquid 
will  moisten  it  and  there  will  be  a  rapid  ebullition,  with  disengage- 
ment of  a  large  amount  of  vapor." 

Hence  many  disastrous  steam  boiler  explosions.  Water 
in  the  condition  now  described  is  said  to  be  in  the  sphe- 
roidal state. 

"  If  a  surface  be  heated,  a  molecule  of  gas  striking  against  it  is 
"heated  ;  it  leaves  the  hot  surface  with  a  velocity  greater  than  that 
with  which  it  had  approached  it.  If  the  surface  be  fixed,  the  gas  in 
front  of  it  is  driven  away  from  it  by  the  bombardment  of  the  mole- 
cules which  have  touched  the  hot  surface  and,  on  their  return,  strike 
their  fellow  molecules  ;  in  front  of  the  hot  surface,  the  gas  is,  there- 
fore, under  a  greater  pressure  than  it  would  have  been  had  the  sur- 
face been  cold.  *  *  *  A  layer  of  particles  in  such  a  condition  is 
called  a  Crookes's  layer.  *  *  *  The  layer  of  aqueous  vapor  be- 
tween water  in  the  spheroidal  state  and  the  heated  surface  is  a 
Crookes's  layer ' ;  particles  strike  the  heated  surface,  rebound  and 
rtrike  the  liquid,  thus  maintaining  a  clear  space  between  the  metal 
and  the  drop!  Ether  and  small  drops  of  bromine  float  in  the  same 
way  on  the  surface  of  hot  water.  A  lump  of  carbonate  of  ammonia 
thrown  into  a  red-hot  platinum  crucible  assumes  the  spheroidal  state 
superficially  but  does  not  melt.  The  hand  can  be  safely  immersed 
in  melted  metal  if  it  be  not  too  dry  and  if  the  immersion  be  effected 
with  a  certain  degree  of  prompt  deliberation  ;  a  Crookes's  layer  of 
water  vapor  intervenes  between  the  hand  and  the  metal. 

"  When  liquid  sulphurous  acid  is  dropped  into  a  white-hot  plati- 
num crucible,  it  sinks  greatly  in  temperature  on  account  of  its  rapid 
evaporation  and  its  slow  reception  of  heat  across  the  Crookes's  layer  ; 
if  a  little  water  be  added  to  it,  the  water  freezes.  Ice  can  thus  be 
produced  in  a  white  hot  platinum  crucible.  A  similar  Crookes's 
layer  is  formed  if  a  quantity  of  solid  carbonic  dioxide  be  lightly 
placed  on  the  tongue  ;  the  extreme  cold  (—  80°  C.)  is  not  felt.  When 
the  hot  solid  body  cools  down,  the  Crookes's  layer  disappears,  the 
liquid  suddenly  comes  in  contact  with  the  solid,  still  relatively  hot, 
and  the  liquid  explodes  in  vapor.  This  occurs,  in  the  case  of  water 
and  iron,  at  about  180°  C." — Daniell. 


[Elements  of  Natural  Philosophy,  pp.  J&S-ML]         217 

§  576.  See  First  Prin.  Nat.  Phil,  Exp.  181. 

§  579.  A  lesser  calorie  is  sometimes  called  a  millecalorio 
or  a  water-gram-centigrade  unit. 

Another  heat  unit  has  been  proposed,  viz.,  the  Electro- 
magnetic Unit.  This  is  the  amount  of  heat  developed  in 
one  second  in  an  electrical  circuit  of  one  ohm's  resi.st;m< m 
by  a  one  ampere  current.  It  is  called  &  joule  and  is  e<jui\ - 
alent  to  10,000,000  ergs  or  10  megergs.    See  §  471. 

§  585.  In  physical  changes,  energy  is  always  conserved, 
none  of  it  is  ever  destroyed.  The  thermal  energy  that  dis- 
appears when  a  body  is  melted  has  not  been  annihilated  ; 
it  is  saved  in  the  liquid  as  potential  energy.  When  a 
liquid  (water,  for  example,)  solidifies,  its  molecules  arrange 
themselves  in  certain  positions  in  accordance  with  their 
mutual  attractions.  When  the  beautiful  crystals  thus 
formed  are  melted,  the  constituent  molecules  are  driven 
into  new  positions  in  opposition  to  these  attractive  forces. 
This  means  that  the  kinetic  energy  thus  expended  has 
been  converted  into  potential  energy  (§  159). 

See  First  Prin.  Nat.  Phil,  Exp.  183. 

§  580.  On  freezing  mixtures,  see  "  Scientific  American 
Supplement,"  No.  89.  On  artificial  ice  machines,  see 
"  Scientific  American  Supplements,"  85  and  91.  See  First 
r  In.  Nat.  Phil,  §383  (b). 

§  587.  Concerning  crystallization  and  flowers  of  ice,  see 
Deschanel's  "  Natural  Philosophy,"  §§  233,  234. 

§  590.  When  water  freezes  under  such  circumstances 
that  it  can  not  expand,  the  freezing  demands  a  lower  tem- 
perature. In  other  words,  pressure  lowers  the  freezing 
point  of  ice.  On  the  other  hand,  pressure  raises  the  tem- 
perature of  substances  that  contract  during  that  change. 

If  pieces  of  ice  be  firmly  pressed  together  they  become  firmly 
united — frozen  together.     Thus,  ice  chips  may  be  moulded  by  heavy 
pressure  into  one  solid,  transparent  mass.     This  welding  pn>< 
called   regolatint   and  depends  u|H>n  the  lowering  of   the    Pn 
1>  >int  by  pressure.     If  heavy  weights  be  hung  at  each  end  of  a  wim 
hanging  over  a  block  of  ice, the  wire  will  slowly  cut  it*  way  tin 


218  [Elements  of  Natural  Philosophy,  pp.  441,  442^ 

the  ice,  regelation  closing  the  cut  behind  the  slowly  advancing  wire 
so  that  at  the  end  of  the  experiment,  the  ice  is  still  one  solid  block 
as  at  first.  The  pressure  brought  the  freezing  point  of  the  particles 
beneath  the  wire  below  the  temperature  of  the  ice.  Consequently, 
they  melted.  The  liquid  particles  passed  above  the  wire,  where 
(there  being  no  pressure  from  the  wire)  the  freezing  point  was  higher 
than  the  temperature  of  the  liquid  particles  which  are  even  colder 
than  the  block  of  ice  from  which  they  were  liquefied.  They,  there- 
fore, froze  again,  firmly  uniting  the  two  parts  of  the  block.  See 
Deschanel's  "  Natural  Philosophy,"  §§  238,  239. 

§  591.  If  a  liquid  be  heated,  under  pressure,  to  a  tem- 
perature above  its  ordinary  boiling  point  (§  569),  there  is  a 
rapid  production  of  vapor  and  remarkable  lowering  of  the 
temperature,  when  part  or  all  of  the  pressure  is  removed. 
Liquid  nitrous  oxide  (N20)  at  0°  C.  is  still  far  above  its 
boiling  point  and  its  vapor  exerts  a  pressure  of  about  30 
atmospheres  (§  277).  If  this  liquid  be  drawn  off  into  an 
open  vessel,  it  boils  with  extreme  violence  but  is  soon 
cooled  to  its  boiling  point  for  the  atmospheric  pressure 
(—  88°  C.)  and  then  boils  away  slowly  while  its  tempera- 
ture remains  at  that  low  point.  See  Elements  of  Chem- 
istry, §  80. 

In  any  case,  the  formation  of  vapor  is  work  and,  there- 
fore, requires  the  expenditure  of  energy.  Whenever  a 
molecule  is  shot  off  from  the  exposed  surface  of  a  liquid 
and  thus  passes  beyond  the  attraction  of  the  molecules  left 
behind  (see  Hand-Book  note  on  §  564),  it  obtains  its  motion 
from  the  energy  of  the  liquid  mass  and  keeps  it  at  its 
expense.  Thus,  as  the  vaporization  goes  on,  the  departure 
of  each  succeeding  molecule  robs  the  still  liquid  mass  of 
part  of  its  molecular  energy,  lessens  its  heat  and  lowers 
its  temperature. 

See  First  Prin.  Nat.  Phil,  Exps.  187,  189,  190. 

§  592.  "  Only  a  certain  amount  of  vapor  can  exist  in  a  given  space 
at  a  given  temperature  (see  note  on  §  564).  If  a  space  saturated 
with  vapor  be  cooled,  some  of  the  vapor  must  condense  into  the 
liquid  state.  Any  diminution  of  the  space  occupied  by  a  saturated 
vapor  will  cause  some  of  the  vapor  to  become  liquid  for,  if  it  do  not 


[Elements  of  Natural  Philosophy,  pp.  U?-446.]         219 

condense,  its  density  and  pressure  must  increase  ;  but  a  saturated 
vapor  is  already  at  its  maximum  density  and  pressure 

"  If  the  vapor  in  a  given  space  be  not  at  its  maximum  density,  its 
ue  will  increase  when  its  volume  is  diminished  until  the  max- 
imum pressure  is  reached;  when,  if  the  temperature  remain  con- 
stant, further  reduction  of  volume  causes  condensation  into  the 
liquid  state  without  further  increase  of  density  or  pressure.  This 
i nt  is  true  of  several  of  the  gases  at  ordinary  temperatures. 
Cblodne,  sulphurous  acid  (SO.),  ammonia,  nitrous  oxide  (Ng0),  car- 
bonic acid  (C02)  and  several  other  gases  become  liquid  under  suffi- 
«i  tot  pressure.  At  a  temperature  of  30.92  C,  pressure  ceases  to 
liquefy  carbonic  acid.  This  is  the  critical  temptrature  for  that  sub- 
stance. The  critical  temperatures  of  oxygen,  hydrogen  and  tin; 
other  so  called  'permanent  gases'  are  so  low  that  it  is  only  by 
methods  capable  of  yielding  an  extremely  low  temperature,  com- 
bined with  great  pressure,  that  they  can  be  liquefied.  By  the  use  of 
such  methods,  any  of  the  gases  may  be  made  to  assume  the  liquid 
state." — Anthony  and  Brack)  tt. 

See  Daniell's  "Principles  of  Physics,"  p.  217. 

§  593.  Liquefaction  is  work  and  requires  the  expendi- 
ture of  energy.  The  quantity  of  thermal  euergy  required 
to  melt  a  unit  mass  of  a  substance  is  the  heat  equivalent 
of  fusion  of  that  substance. 

See  Friers  "  Physical  Technics,"  p.  416. 

§  594.  See  Frick's  "  Physical  Technics,"  p.  437,  and 
Deschanel's  "Natural  Philosophy,"  §  349. 

§  597.  "  The  specific  heat  of  substances  is  not  perfectly  constant 
at  all  temperatures.  Therefore,  there  is  a  necessity  of  the  qualifica- 
tion, '  from  0°  C.  to  1°  C  This  want  of  constancy  is,  among  gases, 
most  remarkable  in  those  which  are  most  condensible  ;  but  among 
solids  and  liquids  the  variations  of  specific  heat  are  still  more  re- 
markable and  indicate  differences  in  the  amount  of  internal  work 
associated  with  changes  of  temperature  at  different  temperature, 
this  internal  work  being  done  in  effecting  changes  in  the  density,  the 
intermolecular  stresses,  the  allotropic  form,  and  so  on." — DanieU. 

The  specific  heat  of  a  body  may,  where  both  the  increments  are 
small,  be  found  by  dividing  the  number  of  calories  supplied  to  unit- 
by  the  increment  of  temperature  produced. 

§  598.  See  Deschanel's  "Natural  Philosophy,"  §§  343,  :*44 
aud  Daniell's  "Principles  of  Physics,"  p.  372. 


220  [Elements  of  Natural  Philosophy,  pp.  446-448.] 

§  600.  The  following  is  known  as  Dulong  and  Petit's 
Law  of  Atomic  Heat  : 

The  product  of  the  specific  heat  by  the  atomic  weight 
of  any  elementary  substance  is  a  constant  quantity,  or 

To  raise  the  temperature  of  an  atom  of  any  element  one 
degree  requires  an  amount  of  heat  which  is  the  same  for 
all  elements. 

This  law  may  be  extended  to  compound  bodies.  For 
all  compounds  of  similar  chemical  composition,  the 
product  of  the  total  chemical  equivalent  by  the  specific 
heat  is  the  same. 

(a.)  The  variations  in  the  last  column  of  the  following  table  are 
within  the  limits  of  experimental  error. 

± .„„„„  SPECIFIC      ATOMIC  WEIGHT.      -^     -_ 

elements.  HEAT         (See  Chemistry.)      PR°DUCT. 

Iron 0.114                 55.9  6.372 

Copper ..  0.095                 63.17  6.001 

Mercury 0.0314  (solid)  199.71  6. 128 

Silver 0.057  107.067  6.137 

Gold 0.0329  196.15  6.453 

Tin 0.056  117.7  6.591 

Lead 0.0314  206.47  6.483 

Zinc 0.0955               64.9  6.198 

(b.)  "  This  product  (the  atomic  heat  of  elements ;  the  molecular 
heat  of  compounds)  has  this  physical  meaning  :  Of  any  substance, 
whose  atomic  or  molecular  weight  we  know,  we  may  take  a  number 
of  grams  numerically  equal  to  the  atomic  or  molecular  weight  ;  e.  g., 
35.5  grams  of  chlorine  or  16  grams  of  marsh  gas;  we  may  call  such 
a  quantity  the  gram-atom  or  the  gram-molecule  of  the  substance. 
The  atomic  heat  or  the  molecular  heat  of  a  substance  is  the  number 
of  lesser  calories  of  heat  necessary  to  raise  the  temperature  of  a 
gram-atom  or  a  gram-molecule  of  the  substance  through  1°  C.  *  *  * 
The  specific  heat  of  a  substance  determines  the  temperature  which 
it  will  assume  when  a  definite  quantity  of  heat  is  supplied  to  it  or 
liberated  in  it." — DanieU. 

Exercises,  Page  448, 

1.  Find  the  number  of  calories  (§  579)  that  may  be 
furnished  by  the  several  quantities  of  water  in  cooling  to 
any  given  temperature,  as  0°  C. 


[Elements  of  JRtfml  Philosophy,  p.  U9-]  221 

1  Kg.  at  40°  gives  40  heat  units. 

2  "  "  30°  *  GO  "  " 

3  "  "  20°  4<  60  "  " 

4  «  "  10°  "  40  "  " 
10  "  "  200  "  " 

These  200  heat  units  would  warm  the  10  Kg.  of  water 
20°  above  the  given  temperature  or  to  20°  C.  It  Qwkefl 
no  difference  what  tempera  lure  be  chosen  for  the  reduc- 
tion. If,  e.  g.,  we  try  a  temperature  of  10°  C,  we  shall 
have  (30  +  40  +  30  +  0  =)  100  heat  units.  This  quan- 
tity of  heat  will  warm  10  Kg.  of  water  10°  above  the  chosen 
temperature  or  to  20°  C.  If  a  still  higher  temperature  be 
chosen  for  the  reduction  and  care  being  given  to  the 
algebraic  signs,  the  result  will  still  be  the  same. 

2.  (See  §  598.)     19.366  x  =  0.634;    x  =  .0327  + . 

Ans. 

3.  (See  §  595  [2.])     85  x  =  80  x  15;    x  =  14.117+. 

Aiis. 

4.  The  specific  heat  of  ice  being  0.5  (§  600  [2.]),  it  will 
require  50  heat  units  to  warm  the  ice  to  the  melting  point 
It  will  require  800  more  to  melt  it.  95  x  =  850  ;  x  = 
$.M.—A7is. 

5.  The  specific  heat  of  steam  is  0.48.  Each  pound  of 
steam,  in  cooling  to  100°  C,  would  yield  12  heat  units. 
These,  with  the  heat  from  condensation  and  cooling  to 
25°  C.  would  yield  (12  +  537  +  75  =)  624  heat  units. 
The  required  quantity  of  steam  must  furnish  624  x  heat 
units.  To  warm  the  ice  to  0°  C,  will  require  20  heat 
units.  This,  with  the  heat  required  for  fusion  and  warm- 
ing the  melted  ice  to  25°  01,  amounts  to  545  heat  units. 

624  x  =  545  ;    x  =  .87  +  .— An*. 

6.  There  will  be  (48  +  537  +  80  =)  665  heat  units 
furnished  by  the  steam.  Each  Kg.  of  mercury  will  require 
(10  x  .0333  =)  .333  heat  units. 

0.333  x  =  665;   x  =  1997.— Ans. 


222  [Elements  of  Natural  Philosophy,  pp.  448,  449.] 

7.  (See  §  593.)    80°  C.—Ans. 

8.  Let  x  =  the  temperature.  Then,  80  +  x  =  10 
(20  —  a?)j    x  —  10.9  + .— Ans. 

9.  The  water  can  furnish  60  heat  units  for  melting 
ice.  This  will  melt  £  of  a  pound  of  ice.  The  result  will 
be  \  lb.  ice  and  of  lb.  of  ice  cold  water. 

10.  The  steam  can  furnish  6370  heat  units  in  cooling  to 
0°  0.  This  heat  must  warm  1010  g.  of  water  and  can 
raise  it  to  (6370  -j-  1010  ==)  6.3°+  C.—  Ans.  Or,  we  may 
let  x  represent  the  temperature.  Then  10(637  —  x)  = 
1000  a;;    x  =  6.3°  +  . 

12.  (See  §  598.)  Iron.        Water. 


Specific  Heat,  0.1138 

Weights,  200. 

Change  of  temperature,  300  —  x 


1. 

1000. 

x 


6828  -  22.76  x  =  1000  x 
x=  6.67  +  .    Ans.,  6.67°+  C. 

13.  Ans.,  0.31 +  . 

14.  .0952  x  300(100  —  x)  =  .505  x  700  x ;  x  = 
7.47  +  .    Ans,,  7.47°  0. 

15.  To  melt  the  snow  will  require  400  heat  units  (ounce- 
centigrade).  The  water  can  furnish  460  such  heat  units 
for  melting  snow.  Hence,  the  snow  will  be  melted  and 
the  water  warmed. 

5(80  +  x)  =  23(20  —  x) ;    x  =  2.14 +  .     Ans.,  2.14°  C. 

1 6.  The  warm  water  gave  up  50  heat  units.  As  the  snow 
was  wet,  its  temperature  must  have  been  0°  C.  (§  543.) 
Let  x  represent  the  weight  of  the  snow,  and  1  —  x  the 
weight  of  the  water  that  made  the  snow  wet.  To  melt  the 
snow  and  warm  it  to  10°  C,  required  90  x  heat  units.  To 
warm  the  water,  required  10(1  —  x)  heat  units.  Then, 
90  x  +  10(1  —  x)  =  50 ;  x  =  J,  The  "wet  snow"  was 
half  snow  and  half  water. — Ans. 

Proof. — The  half  pound  of  snow  would  require  40  heat 


[Elements  of  Natural  PJUUmphy,  p.  449.]  223 

Tinits  to  melt  it  The  pound  of  water  would  then  require 
10  heat  units  to  warm  it  to  10°  C.  The  total  of  heat 
energy  required  is  (40  -f  10  =)  50  units.  This  is  exactly 
the  amount  furnished  by  5  lb.  of  water  in  cooling  from 
20°  C.  to  10°  C. 

17.  150  x  299  x  .0314  =  .0333a;;  x  =  42,291  +,  the 
number  of  grams  of  mercury. — Ans, 

18.  The  water  can  furnish  350  heat  units  for  melting 
the  snow.  This  will  melt  (350  -v-  80  =)  4.375  lb.  of  snow. 
The  result  will  be  1J  lb.  of  snow  in  11 J  lb.  of  ice  cold  water. 


22 4        [Elements  of  Natural  Philosophy,  pp.  450-452.'] 

§  603.  See  Daniell's  "Principles  of  Physics,"  p.  373. 

§  604.  Conductometers  are  instruments  for  illustrating 
differences  in  thermal  conductivity.  The  conductometer 
of  Ingenhaus,  represented  in  the  figure,  consists  of  a  hot 
water  vessel  with  handle  and  pro- 
jecting rods  of  different  metals. 
These  rods  are  coated  with  wax. 
The  distances  to  which  the  wax 
melts  on  the  several  rods  indicate 
their  relative  conductivity.  An- 
other form  of  conduct6meter  con- 
sists of  a  metal  ring  from  which 
radiate  rods  of  various  metals  and 
other  substances,  as  glass,  slate,  etc.  The  extremities  of 
these  rods  have  little  cavities  in  which  bits  of  phosphorus 
are  placed.  The  ring  is  placed  around  the  flame  of  a  lamp, 
heat  is  conducted  along  the  rods  and  ignites  the  phos- 
phorus in  the  good  conductors  and  fails  to  do  so  in  the 
poor  conductors.  See  "  Science  Lectures  at  South  Ken- 
sington," Vol.  II,  Lecture  2  ;  DeschaneFs  "Natural  Phi- 
losophy," §§  328-338  and  Daniell's  "  Principles  of  Physics," 
p.  375. 

§  605.  The  low  conductivity  of  liquids  may  be  illustrated 
with  the  apparatus  shown  in  Fig.  291.  See  First  Prin. 
Nat.  Phil.,  §  394.  Mercury  is  a  good  liquid  conductor  of 
heat.  It  is  a  metal.  Hydrogen  is  the  best  known  gaseous 
conductor.  Many  chemists  think  that  hydrogen  is  a 
metal. 

§  606.  For  the  purpose  of  exhibiting  convection  currents, 
the  apparatus  shown  in  Fig.  291  may  be  used,  the  jacket, 
C,  being  carefully  filled  with  hot  water. 

Fill  a  half  liter  (or  a  pint)  Florence  flask  with  hot  water 
colored  with  ink  or  indigo.  Provide  a  perforated  cork 
carrying  a  short  tube  about  half  a  centimeter  in  diameter. 
Covering  this  tube  with  a  finger,  hold  the  flask  at  the  bot- 


[Elements  of  Natural  Philosophy,  pp.  452-454.]  225 

torn  of  a  deep  pail  of  water.  When  the  finger  is  removed 
from  the  tube,  convection  currents  may  be  seen.  They 
will  continue  for  some  considerable  time.  If  the  flask  be 
held  mouth  downward,  there  will  be  no  convection 
currents. 

§  608.  The  theory  of  a  luminiferous  ether  is  generally 
accepted  by  physicists.  J.  D.  Everett,  Professor  of  Nat- 
ural Philosophy  at  Queen's  College,  Belfast,  says  that  the 
existence  of  this  ether  "is  now  universally  accepted  by 
physicists."  See  DauielPs  "Principles  of  Physics,"  pp. 
218,  219  and  "Encyclopaedia  Britannica,"  article  Ether. 
On  the  other  side  of  the  question,  see  Judge  Stallo's  u  Con- 
cepts and  Theories  of  Modern  Physics,"  pp.  112  et  seq. 

§  G10.  See  First  Prin.  Nat.  Phil,  Exp.  202  and  §  397  a. 
When  the  iron  poker  is  very  hot,  its  energetic  molecular 
vibrations  produce  ether  waves  of  varying  lengths  and 
frequencies  of  vibration.  Some  of  these  waves  are  of  such 
a  length  that  they  constitute  obscure  heat  rays  (§§  617,  718), 
by  means  of  which  the  poker's  warmth  may  be  felt  at  a 
distance  ;  others  are  of  such  a  length  that  they  constitute 
luminous  rays  (§  717),  by  means  of  which  the  poker  is 
visible  ;  still  others  are  so  short  and  quick  that  they  con- 
stitute actinic  or  ultra-violet  rays  (§  719)  and  by  the  aid 
of  these,  the  iron  may  be  photographed.  If  the  iron  be 
intensely  hot,  it  may  emit  so  great  a  proportion  of  violet 
and  blue  light  (short  waves)  that  the  poker  may  be  called 
Ci  blue-hot."  As  the  poker  cools,  the  more  rapid  vibrations 
of  the  iron  molecules  cease  and  the  ultra-violet  ether  waves 
are  no  longer  produced  ;  the  poker  thus  becomes  less  easy  to 
photograph  by  its  own  radiations.  Gradually,  the  violet 
avfl  eease  to  be  emitted  and  the  colorchanges  (§  717),  the 
change  of  color  continuing  as  rays  of  increasing  wave 
li  are  successively  dropped  from  the  train  of  waves 
sent  out  until  finally,  about  the  time  when  the  temperature 
sink-  below  525°  C,  it  ceases  to  radiate  light  and  disap- 
pears from  sight  into  the  darkness.     But  the  longer  and 


226  [Elements  of  Natural  Philosophy,  pp.  454-4S9.] 

less  rapid  waves  that  constitute  obscure  heat  are  still 
emitted  and  may  be  felt  for  some  time  by  the  cooler  hand 
held  near  it.  In  fact,  it  never  ceases  to  radiate  heat  and 
can  not  do  so  until  its  temperature  falls  to  the  absolute 
zero  (§  558). 

§  617.  See  First  Prin.  Nat  Phil.,  Exp.  203  ;  also  Desch- 
anel's  "Natural  Philosophy,"  §§  322-324. 

§  618.  See  §  625  and  Deschanel's  "Natural  Philosophy," 
§  326.  At  the  April  (1886)  meeting  of  the  National 
Academy  of  Sciences,  held  at  Washington,  Prof.  Alfred 
M.  Mayer  stated  that  he  had  obtained  foci  of  dark  rays 
with  a  combination  of  thin  lenses  of  ebonite,  but  the  heat 
of  such  foci  was  not  sufficient  to  inflame  substances. 
From  this,  it  appears  that  ebonite  is  diathermanous  for 
obscure  heat. 

§  619.  See  First  Prin.  Nat.  Phil,  Exp.  205. 

§620.  See  Deschanel's  "Natural  Philosophy,"  §§310, 
311. 

§  621.  See  First  Prin.  Nat.  Phil,  Exp.  204. 

§  622.  When  two  bodies  are  placed  opposite  each  other 
with  the  intervening  ether  (of  which  we  cannot  get  rid 
whether  air  be  present  or  not)  one  of  two  cases  may 
present  itself : 

(1.)  Both  may  be  of  the  same  temperature,  in  which 
case  one  loses  by  radiation  to  the  other  just  as  much 
energy  as  it  gains  from  the  radiation  of  that  other.  As 
the  two  bodies  exchange  radiant  energy  to  the  same  extent, 
there  is  no  change  in  their  relative  temperatures. 

(2.)  One  may  be  hotter  than  the  other.  Then  one 
radiates  a  more  energetic  system  of  ether  waves  than  the 
cooler  one  can  and  thus  loses  more  energy  to  the  other 
than  it  gains  from  that  source.  Consequently,  their  tem- 
peratures finally  become  equal,  after  which  the  exchange 
of    energy   continues   on   equal   terms  for  both,  neither 


[Elements  of  Natural  Philosophy,  pp.  469,  4';o.]         22? 

profiting  by  the  exchange  and  the  temperatures  of  both 
remaining  relatively  the  same. 

Not  only  does  the  fire  warm  the  room ;  the  room  also 
warms  the  fire.  The  sun  warms  the  earth  and  the  earth, 
to  a  less  extent,  warms  the  sun.  The  warming  of  a  colder 
body  by  a  hotter  one  depends  upon  the  difference  of  two 
similar  but  unequally  opposed  actions.  This  law,  that 
bodies  are  always  radiating  and  receiving  energy ;  that  the 
amount  of  radiation  depends  upon  the  temperature  of  the 
radiating  body  and  that  when  the  temperature  of  a  body 
is  constant,  it  is  receiving  as  much  energy  as  it  is  radiating, 
is  known  as  Prevost's  Law  of  Exchanges. 

§  623.  SeeDeschanel's  "Natural  Philosophy,"  §§313-321. 

§  624.  See  First  Prin.  Nat.  Phil,  Exp.  206  and  Hand- 
Book  note  on  §  7tZ. 

§  625.  On  the  subject  of  the  note  following  this  para- 
graph, see  Deschaners  "Natural  Philosophy,"  §325  and 
Tait's  "  Light,"  Chap.  XVI. 


228  [Elements  of  Natural  Philosophy.'] 

Questions,  Page  401. 

1.  Because  our  bodily  sensations  of  warmth  and  cold 
depend  largely  on  the  rapidity  with  which  heat  is  conveyed 
to  the  body  or  from  it.    See  §  540. 

2.  Because  the  watery  vapor  in  the  atmosphere,  being 
diathermanous  to  luminous  heat  (§  618),  allows  the  sun's 
rays  to  pass  freely.  These  rays  heat  the  surface  of  the 
earth,  which  then  radiates  obscure  heat.  The  same  watery 
vapor  is  athermanous  to  these  rays  and  prevents  their  out- 
ward passage.  The  vapor  thus  acts  as  a  trap  in  which  the 
heat  is  caught. 

3.  The  clouds  act  as  a  blanket  to  shut  in  the  earth's 
obscure  rays  and  thus  keep  it  warm. 

4.  See  §  624. 

5.  The  glass  acts  as  did  the  watery  vapor  mentioned 
in  Question  2  above. 

6.  Step  on  them  with  bare  feet  in  a  cold  room  and  you 
will  soon  see  that  the  oil-cloth  and  linen  are  the  better 
conductors. 

7.  Sawdust,  with  its  air-filled  spaces,  is  a  good  non- 
conductor of  heat.     So  are  plaster-of-Paris  and  alum. 

8.  The  woollen  being  a  poor  conductor,  tends  to  keep 
the  intense  heat  from  the  bodies  of  the  workmen.  The 
double  windows  inclose  a  layer  of  non-conducting  air. 

9.  The  surface  of  the  earth  is  heated  chiefly  by  radia- 
tion ;  the  atmosphere,  by  convection.     See  §  605,  a. 


[Elements  of  Natural  Philosophy,  p.  4G2.]  229 

§  627.  Crookes's  Radiometer  is  an  instrument  for  con- 
verting the  energy  of  heat  (generally  derived  from  lumin- 
ous rays)  into  the  energy  of  mechanical  work.  It  consists 
of  a  glass  globe,  containing  a  high  vacuum  and  carrying  a 
vertical  needle  axis  "  on  the  summit  of  which  is  poised  a 
rotating  vane  consisting  of  light  rods  to  the  extremities  of 
which  discs  are  fixed,  each  similarly  blackened  on  one 
side."  Such  an  instrument,  placed  in  light,  has  the  black- 
ened sides  of  its  discs  more  heated  than  the  unblackened 
sides  (§  623) ;  if  the  radiant  energy  be  sufficient,  the  vane 
rotates.  Read  the  quotation  from  Daniell  in  the  Hand- 
Book  note  on  §  573.  In  that  case,  the  heated  surface  was 
supposed  fixed.  Here  the  heated  surface  (the  blackened 
discs)  is  not  fixed  and,  reaction  being  equal  to  action  and 
in  the  opposite  direction,  the  tendency  is  to  drive  tin- 
heated  surface  or  discs  backward,  thus  producing  rotation. 

■  If  the  hot  surface  be  the  front  aspect  of  a  disc,  the  back  of  which 
is,  by  some  means,  kept  cooler  than  the  front,  and  if  this  disc  be 
suspended  in  a  gas,  the  heat  of  the  front  surface  increases  the 
pressure  toward  the  front  and  the  gas  flows  round  to  the  back  of  the 
disc.  Thereafter,  the  disc  is  struck  on  the  hotter  surface  by  fewer 
molecules  with  greater  velocities;  on  the  colder  surface  by  a  greater 
number  of  molecules  with  lesser  velocities ;  thus  there  is  compensa- 
tion ;  the  result  is  that  the  disc  is  equally  pressed  upon  in  front  and 
on  the  back  ;  it  does  not  move. 

"  Let  us  now  suppose  that  the  particles  recoiling  from  the  heated 
surface  do  not  meet  other  (gaseous)  molecules  but  impinge  on  the 
walls  of  the  vessel.  A  layer  of  such  particles  is  a  Crookes's  layer. 
This  will  occur  when  the  gas  is  so  rarified  that  the  mean,  free  path 
of  the  molecules  (§  62)  exceeds  the  distance  between  the  hot  surface 
and  the  walls  of  the  vessel  In  such  a  case  there  is  no  flow  of  gas 
from  the  hotter  surface  toward  the  colder  one :  each  molecule  which 
strikes  the  hotter  surface  and  rebounds  with  a  greater  speed  adds 
independently  to  the  recoil  which  the  hotter  surface  suffers  and,  if 
the  hotter  surface  be  movable,  it  is  driven  backwards.  *  *  When 
the  distance  between  the  discs  and  the  opposite  wall  is  excessively 
small,  the  exhaustion  need  not  be  very  good;  indeed,  the  effect  <>f 
repulsion  may  be  made  manifest  even  in  the  open  air.  *  *  Too 
complete  a  rarefaction  is  not  an  advantage,  for  it  leaves  an  insufficient 
supply  of  working  molecules." — Daniell. 


230  {Elements  of  Natural  Philosophy,  pp.  463-466.] 

§  629.   See  Deschanel's  "  Natural  Philosophy,"  §  356. 

§  630.  See  Deschanel's  "Natural  Philosophy,"  §  357  A. 

The  second  law  of  thermodynamics  is  as  follows  :  When 
heat  is  converted  into  work,  under  the  conditions  that 
exist  on  the  earth's  surface,  only  a  small  part  of  the  heat 
drawn  from  the  source  can  be  transformed.  The  rest  is 
given  to  a  refrigerator  which,  in  some  form,  must  be  an 
adjunct  of  every  heat  engine.  This  still  exists  as  heat  and 
is  wasted  as  far  as  any  useful  effect  is  concerned. 

§  631.  The  experiments  of  Count  Rumford  (see  page 
206)  showed  that  heat  is  transformed  mechanical  energy, 
but  it  was  important  to  show  that  the  heat  evolved  is 
always  proportional  to  the  mechanical  energy  expended. 
Joule  worked  to  this  end  from  1842  to  1849.  By  means 
of  weights,  he  revolved  paddle-wheels  in  a  vessel  of  water. 
Stationary  wings  prevented  the  water  from  taking  a  rotary 
motion  with  the  paddle-wheels.  In  this  way,  the  water 
was  warmed.  The  heat  evolved  was  determined  from  the 
rise  of  temperature  ;  the  energy  expended,  by  the  fall  of 
the  weights.  The  experiment  was  varied  by  using  mercury 
instead  of  water  and  by  revolving  an  iron  plate  upon  a 
fixed  iron  plate  under  water.  The  results  are  remarkably 
concordant  and  indicate  424  kilogrammeters  per  calorie. 
See  Deschanel's  "Natural  Philosophy,"  §  357. 

A  kilogrammeter  equals  98,000,000  ergs.  See  Hand- 
Book  note  on  §  154.  Then,  the  dynamical  equivalent  of 
a  calorie  (424  kilogrammeters)  is  424  times  98,000,000  ergs 
or  41,552,000,000  ergs  as  stated  in  the  text-book. 

§  633.  See  Firrt  Prin.  Nat  Phil,  §  410. 

§634.  See  Deschanel's  "Natural  Philosophy,"  §§  351, 
359,  360  and  Tait's  "Heat,"  §§  45-48. 

At  very  high  temperatures,  compound  substances  are 
separated  into  their  elements.  To  effect  this  separation, 
the  powerful  forces  of  chemical  affinity  must  be  overcome 
and  a  considerable  amount  of  energy  must  be  consumed* 


[FJtuunt*  $f  Natural  PkiJMdpky,  j>]>.    \B6-f71.']  231 

The  principle  <>f  toe  oomwtvalUn)  oi  eneigy  naturally 
leads  us  tosupppSfl  that  this  separation  (called  dissociation) 
requires  an  expenditure  of  energy  equal  to  that  evolved  in 
their  chemical  union,  I.  e.,  that  the  dissociation  of  one 
kilogram  of  water,  for  example,  into  its  elements,  oxygen 
and  hydrogen  (see  Elem.  of  Chem.,  §  40) 
would  require  the  expenditure  of  34,462  calo- 
ries or  an  equivalent  <>f  about  14,611,888 
kilogram  meters. 

§  636.  The  accompanying  figure  represents 
a  piece  of  apparatus  illustrative  of  the  single 
acting  engine.  It  consists  of  a  metal  globe, 
with  cylinder,  piston  and  rod,  and  handle. 
The  globe  is  to  be  partly  filled  with  water  and 
held  over  a  lamp.  The  pressure  of  the  steam 
thus  generated  will  raise  the  piston.  Remove  the  globe 
from  the  lamp  and  throw  upon  it  some  cold  water.  The 
steam  is  quickly  condensed  and  atmospheric  pressure  forces 
the  piston  back  with  vigor. 

Candle  bombs,  which  may  be  had  of  J.  W.  Queen  &  Co.,  at  a 
pmall  price,  afford  the  means  of  illustrating,  in  a  peculiarly  striking 
manner,  the  convertibility  of  heat  energy  into  mechanical  energy. 

§  637.  See  Frick's  "  Physical  Technics,"  p.  439  (§  367). 

§  639.  A  model  of  the  centrifugal  governor  may  be  used 
with  the  whirling  table  (Fig.  7).  See  Frick's  "  Physical 
Technics,"  p.  142. 

§  642.  The  water,  air  and  other  contents  of  the  con- 
denser are  removed  by  an  "  air  pump."  Thus,  part  of  the 
energy  saved  is  expended  in  maintaining  the  vacuum. 

§  643.  The  combustion  of  100  lb.  of  coal  yields  808,000 
heat  unite,  equivalent  fco  L,  123,436; 000  foot-pounds.  An 
engine  at  the  Buffalo  Water  Works,  which  is  considered 
very  economical,  developed  a  power  of  80t48&,638  foot- 
pounds, per  100  lb.  of  00ft]  burned.  For  full  information 
upon  the  steam-engine,  see  Thurston's  "  The  Growth  of 


232  [Elements  of  Natural  Philosophy,  p.  ^7i.] 

the  Steam-Engine. "  With  any  safe  boiler  pressure,  it  is 
impossible,  even  with  a  perfect  engine,  to  convert  into 
work  more  than  about  15  per  cent,  of  the  heat  used. 
Concerning  the  "perfect  engine,"  see  Deschanel's  "Natu- 
ral Philosophy,"  §§  358,  A;  362-393. 

Within  the  last  few  years,  gas  and  petroleum  engines 
have  become  common.  Gas  engines  derive  their  power 
from  the  combustion,  in  the  cylinder,  of  an  explosive 
mixture  of  air  and  coal  gas.  In  the  petroleum  engine,  air 
is  forced  into  the  cylinder  through  a  passage  containing 
crude  petroleum.  The  air  forms,  with  the  vapor  of  the 
petroleum,  an  explosive  mixture  which  is  burned  in  the 
cylinder.  While  there  are  practical  difficulties  connected 
with  the  satisfactory  lubrication  of  the  sliding  parts  under 
the  high  temperatures  to  which  they  are  necessarily  sub- 
jected, they  offer  certain  advantages  as  "  ready  motors  " 
and,  under  some  circumstances,  are  preferable  to  smal[ 
steam  engines. 

All  of  these  engines  are  devices  for  converting  the  po- 
tential energy  of  chemical  separation  (oxygen  and  fuel) 
into  mechanical  energy  through  the  intermediate  form  of 
heat.  But  the  chemical  separation  was  wrought,  at  some 
period  of  the  world's  history,  by  the  energy  of  the  sun- 
beam (vegetable  growth).  Thus,  we  see  that  the  energy 
of  the  engine  is  transformed  solar  radiation. 

See  Daniell's  "Principles  of  Physics,"  p.  367. 

Exercises,  Page  471* 

1.  See  §  631. 

2.  (§  634,  a.)     2,220  -f-  15  =  148.     Ans.,  148  oz. 

3.  5,747  g.  or  5.747  Kg.— Ans. 

4.  34.462°  C—  Ans. 

5.  80  x  1,390  =  111,200,  the  number  of  feet  (in  vacuo) 
that  the  ice  must  fall. 

6.  (80  +  100  +  537)  x  1,390  =  996,630,  the  number  of 
feet. — Ans. 


[Elements  of  Natural  Philosophy,  p.  472.]  233 

7.  8080  x  1390  x  5  +  2000  =  28078,  the  number  of 
feet. — Ans. 

8.  88.42$  of  5  lb.  =  4.421  lb.,  the  quantity  of  carbon. 

5.61$  of  5  lb.  =  .2805  lb.,  the  quantity  of  hydrogen, 
8080  x  1390  x  4.421     =  49653135.2 
34462  x  1390  x     .2805  =  13436561.49 
Total  number  of  foot-pounds,  63089696.69 

63089696.69  -r-  2000  =  31544.8  +  ,  the  number  of  feet 
— Ans. 

n     /c        B  1K*\        15°    X    1920    X    1920     .     OO  OVK* 

9.  (See  §  157.)    j———^  +  32  =  37.o6  +  . 

Ans.,  37J°  F. 

10.  (a.)  If  the  water  were  boiling  hot,  -^ = 

1203.72  +  ,  the  number  of  pounds. — Ans. 

If  the  water  were  ice  cold,  -  — ^,r- =  1014.75, 

bo  7 

the  number  of  pounds. — Ans. 

See  §  634  (b). 

8080xW_x_80  =  lhm_AM 

V   '      2000  x  .1138  T 

11.  1390  x  48  x  (80  +  100  +  537)  =  47838240,  the 
mechanical  equivalent  of  the  heat  expressed  in  foot-pounds. 

«*  =  47838240;  ^~  =  47838240  ;  »  =  392.234. 
Zg  D4.0/4 

Ans.,  392.2  ft.  per  second. 

-.o    ra      Cloo\       8x2000x2000  0  _„, 

12.  (See  §  132.)    ^^  g^— m  -  3.57  +  . 

Ans.,  3.57  lb. 

13.  (a.)  Ans.,  1390  ft.  or  424  meters.     (§  631.) 

(b.)  424  m.  x  .0333  =  14.1192  m.—  A ?is. 

14.  The  weight  makes  no  difference,  as  an  increase  in 
the  weight  would  increase  the  working  power  and  the  work 


234  [Elements  of  Natural  Philosophy,  p.  472.] 

to  be  done  at  the  same  rate.     It  may  be  called  1  gram  (oi 
anything  else). 

That  weight  of  water  heated  100°  would  require  100 
heat  units.  That  weight  of  lead  heated  100°  would  re- 
quire (.0314  x  100  =)  3.14  heat  units,  equivalent  to 
133136  gram-centimeters.    (See  §  600.) 

o-  =  tt^tt  =  133136;    v*  =  260946560  ;    v  =  16153.8. 
2g        1960 

— Ans. 

15.  772000  -h  1390  =  555.4—,  the  number  of  pound- 
centigrade  heat  units.  772000  -^  772  =  1000,  the  num- 
ber of  pound-Fahrenheit  heat  units.     (§  579,  a,  3  and  4.) 

tja    64  x  1400  x  1400       OQO  ■     .,  ,        . - 

16'  6iMlTiMo-^o  =  ^ 

— Ans. 
1W  7  x  1000  x  1000  .-t 

17'  64.32  x  772^70^1138  =  1?'7  +  '  the  number 
of  degrees  Fahrenheit. 

7  x  1000  x  1000 


9.8  +  ,  the  number  of 


64.32  x  1390  x  70  x  .1138 
degrees  centigrade. 

18.  (442  —  374)  x  6  x  .056  =  22.848,  the  number  of  heat 

units  for  heating. 
25.6  x  6  =  153.6      the  number  of  heat 

units  for  melting. 

772  x  176.448  =  136217.856,  the 
number  of  foot-pounds. 

19.  The  weight  of  the  ball  makes  no  difference.  (See 
the  14th  problem  above.)    Call  it,  for  convenience,  1  lb. 

1  ^4.3^x13^  =  16  +  '  the  nUmber  °f  heat  UllitS 
ieveloped. 

Suppose  the  ball  to  be  even  ice  cold.  Its  temperature 
would  have  to  be  raised  326°  C.      This  would  require 


[Elements  of  Natural  Philosophy.]  235 

Review  Questions  and  BM irises,  Page  473. 

1.  (326  x  1.8)  +  32  =  618.8.— A  ru. 

5.37  x  1.8  ==  9.666.— Ans.     (See  §  546.) 

2.  There  is  no  difference.     (See  §  546.) 

3.  760  :  750  )         .  nnA  k  A_  *_■ 
373:473[=4'500:a;-     •*•  *  =  5>631  +  ' 

Atis.,  5,631 -f  cu.  cm. 

4.  27  inches  x  13.6  =  367.2  inches  or  30.6  ft.— Ans. 
{§§  300,  253.) 

10.  (a.)  -  3°  F.  =  —  19*°  C;  77°  F.  =  25°  C. 
(b.)  18°  C.  =  64.4  F.;  20°  C.  =  68°  F. 

11.  273°  C.  See  §§  557,  559. 
13.  Ans.,   1,  t,  -&. 

15.  (a.)  The  424  kilogrammeters  of  energy  would  gen- 
erate one  calorie.     (§  631.) 

16.  (a.)  4,000  -r-  62.42  =  64.08-f,  the  number  of  cubic 
feet.—  Ans.     (See  §  226,  note.) 

(b.)  64.08  -r-  1.09  =  58.78  +  ,  the  number  of  cubic 
feet. — Ans. 

17.  30  inches  x  13.6  x  -^  =  510  in.  or  42J  ft.—  Ans. 

22.  (a.)  273  :  283  =  546  :  566. 

566  cu.  cm.  —  546  cu.  cm.  =  20  cu.  cm.,  the  expansion. 

,.      64.32  x  50  x  50 

(*•)  aJ"qo =  2,500,  the  number  of  foot- 

pounds.     (§  157,  a.) 

23.  100  x  .1138  =  11.38,  the  number  of  heat  units  re- 
quired.    (§  579,  a,  3.) 

1390  x  11.38  =  15,818.2,  the  number  of  foot-pounds 
RMjuind.     (§  631.) 

To  lift  7  T.  of  iron  1  ft.  would  require  only  14,000  foot- 
pounds. 


CHAPTER  IX. 

§  644.  The  idea  of  a  luminiferous  ether  (§  608)  exist- 
ing  and  acting  as  a  carrier  of  motion  must  be  clearly 
formed  and  constantly  maintained.  Our  physical  sensa- 
tions result  from  motion  acting  upon  the  nerves.  One 
kind  of  motion  is  competent  to  excite  one  nerve ;  another 
kind,  another  nerve,  etc.  The  peculiar  kind  of  motion  im- 
posed upon  the  ether  by  the  vibrating  molecules  of  a  lumi- 
nous body  and  transmitted  by  the  ether  to  the  retina  of  the 
eye  awakens  the  sensation  of  sight. 

The  difference  between  a  longitudinal  and  a  transversal 
wave  may  be  made  more  clear  by  imagining  two  rays,  one 
of  sound  and  one  of  light,  to  come  from  directly  over- 
head, i.  e.f  vertically  downward.  In  the  former  case,  the 
vibrations  will  all  be  vertical,  while  in  the  second  case 
they  will  all  be  horizontal.  Concerning  the  corpuscular 
or  emission  and  the  undulatory  theories  of  light,  see  Tait's 
"Light,"  §§  31-34  and  205-220  and  Stokes's  " Nature  of 
Light,"  Lecture  I. 

"  While  I  have  endeavored  to  place  before  you,  with  the  utmost 
possible  clearness,  the  basis  of  the  undulatory  theory,  do  I  therefore 
wish  to  close  your  eyes  against  any  evidence  that  may  arise  of  its 
incorrectness  ?  Far  from  it.  Yon  may  say,  and  justly  say,  that  a 
hundred  years  ago  another  theory  was  held  by  the  most  eminent 
men,  and  that,  as  the  theory  then  held  had  to  yield,  the  undulatory 
theory  may  have  to  yield  also  This  is  perfectly  logical.  Just  in  the 
same  way,  a  person  in  the  time  of  Newton,  or  even  in  our  own  time, 
might  reason  thus  :  '  The  great  Ptolemy,  and  numbers  of  great  men 
sifter  him,  believed  that  the  earth  was  the  centre  of  the  solar  system. 
Ptolemy's  theory  had  to  give  way  and  the  theory  of  gravitation  may, 
in  its  turn,  have  to  give  way  also.'  This  is  just  as  logical  as  the 
former  argument.  The  strength  of  the  theory  of  gravitation  rests 
on  its  competence  to  account  for  all  the  phenomena  of  the  solar 
system.     On  a  precisely  similar  basis  rests  the  undulatory  theory  of 


[Elements  of  Natural  Philosophy,  pp.  475,  4:0.]  .'!. 

lijrht  ;  only  that  the  phenomena  which  it  explains  are  far  more  varied 
and  complex  than  the  phenomena  of  gravitation." — Tymhiil. 

"  That  light  is  not  itself  a  substance  may  be  proved  from  the 
phenomenon  of  interference.  A  beam  of  light  from  a  single  pMUPM 
is  divided  by  certain  optical  methods  into  two  parts,  and  th»\s<\  after 
travelling  by  different  paths,  are  made  to  reunite  and  fall  u|>on  a 
screen.  If  either  half  of  the  beam  is  stopped,  the  other  falls  upon 
the  screen  and  illuminates  it,  but  if  both  are  allowed  to  p;i 
screen  in  certain  places  becomes  dark  and  thus  shows  that  the  two 
portions  of  light  have  destroyed  each  other  (see  §  713).  Now  we 
cannot  suppose  that  two  bodies  when  put  together  can  annihilate 
each  other  ;  therefore,  light  cannot  be  a  substance.  What  we  have 
proved  is  that  one  portion  of  light  can  be  the  exact  opposite  of  an- 
other portion,  just  as  +  a  is  the  exact  opposite  of  —  «,  whatever  a 
may  be.  Among  physical  quantities  we  find  some  which  are  capable 
of  having  their  signs  reversed  and  others  which  are  not.  Thus  a 
displacement  in  one  direction  is  the  exact  opposite  of  an  equal  dis- 
placement in  the  opposite  direction.  Such  quantities  are  the  meas- 
ures, not  of  substances,  but  always  of  processes  taking  place  in  a 
substance.  We  therefore  conclude  that  light  is  not  a  substance  but 
a  process  going  on  in  a  substance,  the  process  going  on  in  the  first 
portion  of  light  being  always  the  exact  opposite  of  the  process  going 
on  in  the  other  at  the  same  instant,  so  that  when  the  two  portions 
are  combined,  no  process  goes  on  at  all." — Encyclopaedia  Britannica, 
Vol.  8,  p.  569  (ninth  edition). 

The  difficulties  that  encumber  the  undulatory  theory  of 
light  are  set  forth  at  the  bottom  of  p.  571  of  the  volume 
from  which  the  above  quotation  was  made,  under  the 
heading  Electromagnetic  theory  of  light,  which  see. 

§  645.  Concerning  sources  of  light,  see  Tait's  "  Light," 
SS  M-30. 

§  646.  When  ether  waves  fall  upon  a  body  and  pass 
through  it,  they  are  still  propagated  by  the  ether  that  lies 
between  the  molecules.  With  respect  to  the  transmission 
of  obscure  heat  rays  (§§  617,  718),  bodies  are  diatherma- 
nous  or  athermanous  ;  with  respect  to  luminous  rays 
(§  717),  they  are  transparent  or  opaque;  with  respect  to 
actinic  rays  (§  719),  no  special  terms  are  yet  in  use.  A 
perfectly  transparent  body,  like  colorless,  thin  glass  with 


238  [Elements  of  Natural  Philosophy,  p.  476.] 

a  polished,  clean  surface,  is  invisible  by  the  light  that 
passes  through  it  though  the  presence  of  the  glass  may  be 
manifested  by  reflected  light.  For  example,  the  sunlight 
reflected  by  the  windows  of  a  distant  house  may  make  the 
glass  magnificently  visible. 

If  glass  be  roughened  or  ground,  the  numerous  facets 
thus  produced  reflect  light  and  make  the  glass  visible 
from  all  directions.  Transmitted  light  is  irregularly  turned 
from  its  path  so  that  while  light  passes  through  the  glass, 
objects  can  not  be  clearly  seen  through  it.  Such  glass  is 
translucent.  When  the  glass  is  powdered,  it  presents  so 
many  facets  and  reflects  the  light  so  often  that  the  energy 
of  the  ether  waves  becomes  entangled,  as  it  were,  in  the 
molecules  of  ordinary  matter  and  fails  to  find  a  passage 
through.  Glass  powder  is,  therefore,  opaque.  In  such 
cases,  the  ether  loses  energy,  ordinary  matter  gains  it  and 
the  body  is  heated. 

"  When  a  succession  of  waves  impinges  on  a  mass  of  ordinary 
matter,  the  effect  varies  according  to  the  nature  and  the  condition  of 
the  body  which  receives  their  shock;  if  it  be  an  ordinary  opaque 
mass,  that  mass  may  be  warmed,  the  energy  of  wave  motion  being 
transformed  into  heat ;  and  the  waves  which  have  impinged  upon 
the  opaque  mass  are  ex  post  f ado  called  a  beam  of  radiant  heat  ;  if 
they  fall  upon  the  eye,  they  may  produce  a  sensation  of  light  and  the 
wave  system  is  then  called  a  beam  of  light  ;  falling  upon  a  sensitized 
photographic  plate  or  a  living  green  leaf,  it  may  operate  chemical 
decomposition  and  it  is  then  called  a  beam  of  actinic  rays.  Hence 
we  speak  of  heat  rays,  of  light  rays  and  of  chemical  or  actinic  rays 
(§§  717-719),  these  names  being  given  to  one  and  the  same  train  of 
waves  according  to  the  effect  which  it  is  found  competent  to  produce. 
But  while  ether  waves  are  in  course  of  traversing  the  ether,  there  is 
no  heat,  light  or  chemical  decomposition  ;  merely  wave  motion  and 
transference  of  energy  by  wave  motion." — Daniell. 

§  649.  "  It  is  very  remarkable  to  find  how  slowly  the  human  race 
have  reached  some  even  of  the  simplest  facts  of  optics.  We  can 
readily  understand  how  constant  experience  must  have  forced  on 
men  the  conviction  that  light  usually  moves  in  straight  lines — i.  e., 
that  we  see  an  object  in  the  direction  in  which  it  really  lies.  But 
how  they  could  have  believed  for  ages  that  objects  are  rendered 
visible  by  something  projected  from  the  eye  itsel  f — so  that  the  organ 


[Elements  of  Natural  Philosophy,  pp.  476-4SO.]  239 

of  sight  was  supposed  by  the  most  enlightened  of  them  to  be  analo- 
gous to  the  tcntacula  of  insects,  and  sight  itself  a  mere  species  of 
touch — is  most  puzzling.  They  seem  not  till  about  350  B.  C.  to  have 
even  raised  the  question,  -  If  this  is  how  we  see,  why  cannot  we  see 
in  the  dark?  or,  more  simply, — What  is  darkness?  The  former  of 
these  questions  appears  to  have  been  first  put  by  Aristotle." — Tait. 

§  650.  See  Friek's  "Physical  Technics,"  p.  209  (§  181) 
and  Deschanel's  "Natural  Philosophy,"  §  748. 

"  Another  beautiful  illustration  is  easily  obtained  by  cutting  with 
a  sharp  knife  a  very  small  T  aperture  in  a  piece  of  note  pa; N t. 
Place  this  close  to  the  eye,  and  an  inch  or  so  behind  it  place  another 
piece  of  paper  with  a  fine  needle  hole  in  it.  The  light  of  the  sky 
passing  through  the  needle  hole  forms  a  bright  picture  of  the  T  on 
the  retina.  The  eye  perceives  this  picture,  and  in  consequence  re- 
ceives the  impression  of  the  T  much  magnified,  but  turned  upside 
down."— Tail. 

§  653.  See  Deschanel's  "  Natural  Philosophy,"  §§  685- 
G88  A  and  Tait's  *  Light,"  chap.  VI,  for  good  descriptions 
of  the  various  methods  for  determining  the  velocity  oi 
light.  Foucault's  experiment,  therein  described,  was  per- 
formed in  1850  and  showed  a  velocity  of  298,000,000  m., 
as  stated  in  the  text.  In  1879,  Prof.  Miohelson,  slightly 
modifying  the  Foucault  method,  made  at  Annapolis  a  new 
determination  which  exceeded  in  accuracy  anything  ever 
done  before.  Michelson's  Annapolis  result  is  299,910  Km. 
(or  299,910,000  m.).  In  the  meantime,  Prof.  Newcomb  had 
secured  a  government  appropriation  of  $5,000.  He  secured 
the  co-operation  of  Michelson  and  in  the  years  1881,  1882 
and  1883,  two  independent  series  of  observations  Avere 
undertaken,  one  at  Washington  by  Prof.  Newcomb  and  one 
at  the  Case  School  of  Applied  Sciences  at  Cleveland,  0.,  by 
Prof.  Michelson.  XcwcomVs  result  is  299,860  Km. ;  Michel- 
son's  is  299,853  Km.  "The  accordance  is  surprisingly 
close,  far  less  than  the  probable  error  which,  according  to 
Prof.  Newcomb,  may  easily  be  25  or  30  Km."  He  thinks 
that,  with  the  help  of  past  experience  and  without  auy 


240  [Elements  of  Natural  Philosophy,  p.  480,  4SI.] 

radical  change  in  the  apparatus,  a  precision  of  5  or  10  Km. 
can  be  attained. 
J.  E.  H.  Gordon,  on  p.  120  of  his  "  Electric  Induction, " 


•  In  air  and  vacuum  the  velocities  of  light  and  electromagnetic  in- 
duction are  sensibly  equal."  "  In  both  cases,  a  disturbance  is  propa- 
gated through  the  ether."  He  considers  this  "a  very  strong  argu- 
ment for  considering  that  the  electric  and  the  optic  ethers  are  identical, 
for  the  velocity  with  which  a  wave  is  propagated  in  a  medium  is  a 
measure  of  the  density  and  elasticity  of  that  medium."  It  will  be 
well  for  the  teacher  to  study  these  "  Four  Lectures  on  Electrostatic 
Induction,"  carefully. 

§  654.  This  law  is  strictly  true  only  when  the  source  of 
light  is  a  luminous  point.  If  the  rays  be  parallel,  there 
will  be  no  variation  in  intensity,  excepting  so  far  as  may 
be  due  to  the  absorption  of  light  by  the  medium  that  it  is 
traversing.  If  the  rays  be  converging,  the  intensity  will 
increase  toward  the  focus. 

A  bright  spot  that  may  practically  represent  a  luminous 
point  may  be  provided  by  making  a  small  hole  in  a  metal 
screen  and  placing  a  drop  of  glycerin  in  the  hole.  The 
glycerin  will  form  a  double  convex  lens  of  short  focus. 
When  a  sunbeam,  concentrated  by  a  lens,  is  thrown  upon 
the  glycerin,  an  intensely  bright  spot  of  light  appears  on 
the  other  (the  dark)  side  of  the  screen.  This  focus  of  the 
glycerin  lens  may  be  used  as  a  source  of  light  for  many 
experiments.  Similarly,  the  rays  of  an  electric  lamp  may 
be  converged  by  an  achromatic  lens  of  very  short  focus,  as 
the  high  power  objective  of  a  microscope. 

The  intensity  of  light  illumi- 
nating a  surface  is  proportional 
to  the  area  of  the  cross-section 
which  the  surface  presents  to  the 
direction  of  radiation.  In  the 
figure,  let  the  horizontal  lines 
represent  rays  of  light  from  a 
source  (e.  g.,  the  sun)  so  distant 


[Wnnent*  of  Natiini"  PkBrtuphy,  p.    f*/.]  241 

that  the  rays  may  be  considered  parallel.  Some  of  these  rays  fall 
u|k»:i  a  screen,  A  B,  which  l>cing  placed  perpendicular  to  the  rays, 
reeetaet  the  greatest  possible  amount  of  light.  If  the  screen  be  placed 
in  the  position  represented  by  A  B" ,  it  will  evidently  receive  fewer 
r  th<»se  previously  received  by  A  C,  which  represents  the  cross- 
BectloD  which  the  screen  now  presents  to  the  direction  of  the  rays. 
But  if  the  light  which  illuminated  .1  0  be  diffused  over  the  gn-at.  i 
surfac  .1  />' .  the  intensity  must  be  correspondingly  diminished. 
This  explains,  in  great  part,  why  the  heat  of  the  sun  is  less  intense 
(§  644)  at  morning  and  evening  than  at  noon  ;  in  winter  than  in 
summer  ;  at  the  poles  than  at  the  equator. 

A  photometer  is  an  instrument  for  measuring  the  inten- 
sity of  light.  The  simplest  is  Bunsen's,  which  consists  of 
a  sheet  of  white  porous  paper,  with  a  grease  spot  in  the 
middle. 

If  the  paper  be  placed  between  the  eye  and  a  lamp,  the 
spot  will  appear  lighter  than  the  rest  of  the  paper.  If  the 
Jamp  be  placed  between  the  eye  and  the  paper,  the  spot 
will  appear  darker  than  the  rest  of  the  paper.  Illumina- 
tion from  the  rear  makes  the  spot  appear  lighter;  illumina- 
tion from  the  front  makes  it  look  darker.  The  spot  may 
he  placed  between  two  lamps,  so  that  the  illumination  from 
the  rear  will  just  equal  the  illumination  from  the  front ; 
the  spot  will  then  disappear.  The  lights  then  falling  upon 
the  two  surfaces  are  equal  in  intensity.  Suppose  that  a 
candle  be  placed  at  a  distance  of  one  foot  from  the  paper, 
and  that  a  lamp  on  the  other  side  be  moved  back  and  forth 
until  a  place  be  found  at  which  it  causes  the  spot  to  dis- 
appear. Suppose  the  lamp  now  to  be  three  feet  from  the 
paper.  Then  will  the  intensity  of  the  lamp  light  be  nine 
that  of  the  candle  light  If  the  spot  disappear  when 
the  lamp  is  at  a  distance  of  four  feet,  the  intensities  of  the 
lights  will  be  as  l2  to  42  or  as  1  to  16,  varying  inversely 

uares  of   the  distances.      See  Flick's  "Pin 
Technics,"  p.  lsi.  and  DeschaneVs  "Natural  Philosophy." 

at.  Phil,  §  428  (a)  and  (b). 


242  {Elements  of  Natural  Philosophy. ,] 


Exercises,  Page  482. 

1.  The  diameter  of  the  shadow  will  be  5  times  that  of 
the  coin.  The  area  of  the  shadow  will  be  25  times  that 
of  the  coin. 

3.  (c.)  See  §  608. 

4.  (p.)  See  §  649. 

5.  22 :  62  =  1  :  9.—Ans.,  9  candle  power. 

§  655.  See  Frick's  "  Physical  Technics,"  pp.  183-189 ; 
Mayer  and  Barnard's  little  book  on  "  Light,"  pp.  16-26. 

§  656.  See  First  Prin.  Nat  Phil,  Exp.  212. 

§  658.  See  Tyndall's  "  Fragments  of  Science,"  p.  280. 

§  659.  "  We  are  liable  to  deception  by  trusting  to  the  direct  or 
uncontrolled  evidence  of  our  senses.  Some  of  the  most  perfect  illu- 
sions which  have  ever  been  contrived  depend  solely  upon  the  obvious 
fact  that  the  eye  (or  any  other  organ  of  sense)  can  inform  us  only  as 
to  what  reaches  and  affects  it  ;  not,  in  any  way  whatever,  of  whence 
or  how  that  which  affects  it  managed  to  reach  it." — Tait. 

§  660.  In  other  words,  the  image  of  any  point  (in  a  plane 
mirror)  may  be  found  by  drawing  a  line  from  the  point 
perpendicular  to  the  mirror  and  producing  it  to  twice  its 
length. 

§  663.  Two  mirrors  attached  to  each  other  so  as  to  form 
an  angle  that  is  a  submultiple  of  360°,  are  often  used  by 
designers  for  obtaining  symmetrical  patterns.  The  optical 
toy,  called  the  kaleidoscope,  is  constructed  on  the  same 
principle.  See  Deschanel's  "  Natural  Philosophy,"  §§  700- 
705. 

§  672  (a).  For  a  description  of  the  pretty  experiment 
of  the  phantom  bouquet,  see  Deschanel's  "  Natural  Philos- 
ophy," §  712. 


[Element*  of  Natural  Philosophy.] 


■iv.\ 


Exercises,  Faye  498. 

1.  Forty- five  degrees. 

-.'.  Make  an  accurate  diagram.  The  conjugate  focus  will 
he  on  the  principal  axis,  36  inches  from  the  mirror. 

n.   (a.)  See  §  660.     (b.)  See  §  665. 

7.  See  §674. 

8.  He  cannot  in  either  case.  Whatever  his  position, 
the  image  will  appear  as  far  back  of  the  mirror  as  the  man 
is  in  front  of  it,  and  the  part  of  the  mirror  used  to  give  a 
complete  image  will  be  half  the  length  of  the  man.  If 
the  mirror  is  not  half  the  length  of  the  man,  it  can  not 
give  a  full  length  image  of  him,  no  matter  what  his  dis- 
tance from  it.     Let  M  X  represent  the  mirror,  A  B  the 


c               a 

6 

A 

fl 

J 

^ 

^^ 

^=^ 

-  ■ 

^^ 

>-**-^ 

( 

V 

I 

5T                              J 

J 

L> 

man,  and  a  b  his  image.  The  triangles,  A  e  i  and  A  a  b,  are 
similar  and  A  e  =  \  A  a;  therefore  e  i  =  {  A  B.  But 
e  i  is  the  part  of  the  mirror  used  in  forming  the  image. 
Suppose  now  the  man  to  move  either  way,  as  to  C  D.  The 
image  appears  at  c  d  and  C  e  =  |  C  c.  Hence,  n'=  \cd 
or  \  C  D.  Wherever  he  stands,  he  can  not  see  his  com- 
plete image  unless  the  length  of  the  mirror  is  half  his  own 
length  ;  if  it  is  too  short  in  one  case,  it  will  be  too  short 
in  every  such  case. 

9.  Sixty  degrees. 


244 


[Elements  of  Natural  Philosophy,  p.  499.] 


10.  Let  M  N  represent  the  mirror;  E  E'  the  two  eyes 
and  e  e '  the  two  images  of  the  eyes.  Of  course,  E  E'  are 
in  the  same  horizontal  line.  When  E'  is  closed,  E  sees  the 
image  of   E'   at  e'.     Placing  the  wafer  at   W,  hides  e'. 

When  E  is  closed,  E' 
would  see  the  image  of  E 
at  e,  were  it  not  for  the 
wafer  which  hides  it.  See 
§  662.  By  drawing  the 
parallelogram,  E  E'  e'  e, 
and  remembering  that  M 
N  is  midway  between  E 
E'  and  e  e',  it  may  be 
proved,  geometrically,  that 
Ee'  and  E'  e  will  inter- 
sect at  W  as  represented  in  the  figure. 

11.  Construct  the  figure.    See  Fig.  340. 


[Elements  of  Natural  Philosophy,  pp.  500,  501.]  %  I B 


§676.  See  Ma\er  and  Itaniard's  "light/1  pp.  59-91; 
Frick's  "Physical  Technics."  pp.  189-201  Hid Desehanel's 
"Natural  Philosophy,"  §  Wk 

§  678.  The  ratio  that  is  called  the  index  of  refraction  is 
constant^  for  any  two  given  media,  whatever  the  angle  of 
incidence.  The  relative  positions  of  the  incident  and  the 
refracted  rays  may  be  represented  by  the  apoaratus 
represented  in  the  accom- 
panying figure,  which  may 
be  used  either  as  a  moving 
diagram  or  as  a  means 
of  experimentally  verify- 
ing the  law. 

B'  is  a  slider  travelling 
up  and  down  a  vertical 
stem.  A  C  and  B  C  are 
two  rods  pivoted  on  a 
fixed  point,  B,  of  the  ver- 
tical stem.  C  B'  and  C 
B'  are  two  other  rods 
jointed  to  the  former  at 
C  and  C,  and  pivoted  at 
their  lower  ends  on  the 
centre  of  the  slider.  B  C  is  equal  to  B'  C\  and  B  C  to 
B'  C.  Hence  the  two  triangles,  BOB'  and  B  C  By  are 
equal  to  one  another  in  all  positions  of  the  slider,  their 
common  side,  B  B',  being  variable,  while  the  other  two 
sides  of  each  remain  unchanged  in  length  though  altered 


in  position.     The  ratio 


BC        B  C 


or 


is  made  equal  to  the 


CB'  ~   C  B 

index  of  refraction  of  the  liquid  in  which  the  observation 
is  to  be  made.  For  water  and  air,  the  index  is  |  (or  1.336). 
If  the  apparatus  be  immersed  in  water  to  the  level  of  B, 
ABC  will  represent  the  path  of  a  ray  and  C  will  appear 
to  be  in  a  straight  line  with  A  and  B. 


246         [Elements  of  Natural  Philosophy,  pp.  501,  502.] 


The  difference  between  the  angle  of  incidence  and  the  angle  of 
refraction  measures  the  amount  of  bending  of  the  ray  and  is  called 
the  deviation.  These  two  angles  and  the  deviation  increase  or  de- 
crease together.  The  path  of  the  refracted  ray  may  be  constructed 
as  follows  :  Suppose  the  ray  to  pass  from  air  into  water.  Let  B  A 
represent  the  surface  of  the  water  and  C  0  the  direction  of  the  inci- 
dent ray.  Measure  0  A  and  0  B,  as  4  and  3  equal  parts,  e.  g.,  centi- 
meters or  inches.  The  ratio  between 
0  A  and  0  B  slumld  represent  the 
index  of  refraction  for  the  given 
media.  In  this  case,  it  is  f  or  1.33. 
At  A,  erect  a  perpendicular  cutting 
the  line,  0  C,  at  H.  At  B,  let  fall 
the  perpendicular,  B  K.  From  0 
as  a  centre,  with  a  radius  equal  to 
O  H,  describe  an  arc  cutting  B  K  at 
D.  Draw  0  D  which  will  represent 
the  path  of  the  ray  in  the  water. 
From  the  above,  it  will  be  easily 
seen  how  to  construct  the  path  when 
the  wave  passes  from  the  water  instead  of  into  it. 

The  same  result  may  be  obtained 
as  follows  :  Given  the  ray  in  air 
0  0 ;  lay  off  upon  it  4  equal  parts 
starting  at  0,  the  point  of  incidence. 
Through  H,  3  units  distant  from 
0,  draw  A  E,  perpendicular  to 
0  N,  the  refracting  surface.  From 
0  as  a  centre,  with  a  radius  of  4 
units,  draw  an  arc  cutting  this 
perpendicular  at  E.  Draw  the 
straight  line,  E  0  D.  0  D  will 
represent  the  position  of  the  ray 
iia  the  water. 

§  679.  The  figure  on  the  next  page  represents  a  piece  of 
apparatus  very  convenient  for  showing  many  of  the  phe- 
nomena of  refraction  as  well  as  of  total  reflection  (§  681). 
It  consists  of  a  circular  tank  about  18  inches  in  diameter, 
with  a  glass  side.  It  is  graduated  at  its  circumference  and 
furnished  with  a  mirror  adjustable  at  any  point  on  the 
circumference.    This  mirror  reflects  a  beam  of  light  to  the 


[Element*  of  Natural  Philosophy,  p.  50*.]  2 17 

centre  of  the  tank  which  is  filled  with  water  to  its  hori- 
zontal d  iame ter.  See  Frick's  * '  Physical  Technics,"  pp.  1 90- 
192. 

In  the  application  of  the  second  and  third  laws,  it  is 
sometimes  necessary  to  distinguish  between  specific  gravity 


and  optical  density.  The  nature  of  the  transparent  body 
has  a  retarding  effect  on  the  velocity  of  the  transmitted 
light  (§  683).  More  than  this,  each  transparent  substance 
has  its  own  rate  of  transmission  for  ether  vibrations  of 
each  particular  wave  length  and  this  is  found,  in  each  case, 
only  by  experiment.  Some  substances  transmit  ether 
waves  more  rapidly  than  do  some  other  substances  that  are 
less  dense.  For  example,  light  travels  more  rapidly  throng)] 
water  than  it  does  through  alcohol  or  turpentine,  although 
both  alcohol  and  turpentine  are  lighter  than  water.  On 
account  of  this  greater  retardation  of  ether  waves,  these 
lighter  substances  have  a  greater  index  of  refraction  than 
water  has ;  they  are  said  to  be  optically  denser. 


248  [Elements  of  Natural  Philosophy,  pp.  602-507.] 


§  680.  See  First  Prin.  Nat.  Phil,  Exp.  223.  In  the 
first  century  of  the  Christian  era,  Cleomedes  performed 
this  coin  and  cup  experiment  and  showed  that,  in  a  similar 
way,  the  air  may  render  the  sun  visible  to  us  while  it  is 
still  below  the  horizon. 

§  681.  See  First  Prin.  Nat.  Phil,  Exp.  227. 

§  682.  The  optical  illusion  known  as  mirage  is  explained 
in  Deschanel's  "Natural  Philosophy,"  §  726.  It  is  a  result 
of  total  reflection  by  the  atmosphere  and  is  often  seen  in 
hot  countries,  especially  the  Sahara  in  Africa.  See 
Deschanel's  "Natural  Philosophy,"  §  819. 

§  683.  The  text  refers  to  the  First  Prin.  Nat.  Phil, 
§  443,  a.  In  addition  to  the  illustration  of  marching 
soldiers  there  given,  the  following  may  be  used  to  show 
that  a  change  of  wave-front  necessitates  a  change  in  the 
line  of  propagation  : 

"  Suppose  two  persons  are  pushing  a  two-wheeled  cart  along  by 
turning  the  wheels.  If  one  turns  his  wheel  faster  than  the  other 
does,  the  direction  in  which  the  cart  travels  will  be  changed." 

Concerning  a  method  of  proving  that  light  moves  more 

slowly  in  glass  than  it  does  in  air,  see  Tait's  "  Light,"  §  233. 

§  686.  The  angle  formed  by  the  meeting  of  the  two 

refracting  sides  of  a  prism  (or  of  their  planes  produced) 

is  called  the  refracting  angle  of  the  prism  or,  simply,  the 

angle  of  the  prism.     The 
\  construction  for  a  ray  re- 

fracted by  a  prism  may 
be  done  as  follows  : 

Assume  the  index  of  refrac- 
tion to  be  §  (=1.5.  See  §  678/0. 
Let  E  F  H  represent  a  section 
of  the  prism  with  the  refract- 
ing angle  at  E.  Assume  b  c  to 
be  the  path  through  the  prism. 
We  are  required  to  find  the  di- 
rection of  the  ray  on  either  side 
of  the  prism.  Draw  E  B  par- 
allel   to    6  c   and    make  it  3 


[Elements  of  Natural  Philosophy,  p.  507.]  24$ 

units  long  (e.  g.,  3  centimeters  or  inches).  Produce  H  E  in- 
definitely. From  B,  draw  B  M  perpendicular  to  H  E  produced 
and  draw  B  N perpendicular  to  EF.  From  E&s  a  centre,  with  a  radius 
of  two  units,  describe  an  arc  cutting  B  M  and  B  N  at  C  and  A  re 
sjjectively  as  shown  in  the  figure.  From  b,  draw  6  a  parallel  to 
A  /.',  to  represent  the  incident  ray,  and  from  c  draw  c  d,  to  represent 
the  emergent  ray.    Then  will  abc  d- represent  the  refracted  ray. 

In  case  the  construction  proves  impossible,  it  may  be  understood 
that  the  position  assumed  for  b  c  is  more  divergent  from  F  H  than  is 
possible.  Try  the  construction  with  an  equilateral  triangle  as  the 
section  of  the  prism  and  with  b  e  making  a  right  angle  with  E  H. 
You  will  find  that  you  can  not  locate  the  points  A  and  C.  To  show 
that  this  is  an  impossible  position  for  b  c,  we  have  only  to  imagine 
the  ray  moving  in  the  other  direction,  i.  e.,  from  e  toward  b  and 
thence  into  the  air.  Under  such  circumstances,  the  angle  of  inci- 
dence at  b  would  be  60°,  which  largely  exceeds  the  critical  angle  for 
glass  and  air  (?j  682).  The  ray  could  not,  under  such  circumstances, 
emerge  from  the  glass  at  b  but  would  be  reflected  back  into  the  glass 
from  the  face  E  F.  Conversely,  if  a  ray  moving  in  the  direction 
assumed  for  c  b  can  not  pass  from  glass  to  air,  it  is  impossible  for  a 
ray  entering  the  glass  from  the  air  to  take  the  direction  indicated 
by  be. 

See  Hand-Book  note  on  Ex.  9,  page  515  of  text-book. 

Next,  given  a  b,  the  direction  of  the  incident  ray,  to  find  the  di- 
rection  of  the  two  refracted  rays.  From  E,  draw  E  A,  parallel  to 
a  6,  and  make  it  2  units  long,  or  draw  the  arc  from  A' as  a  centre  with 
a  radius  of  2  units  as  shown  in  the  figure  on  the  page  last  preceding. 
Through  A,  draw  A  If  perpendicular  to  2?i^and  of  indefinite  length. 
From  Ebbb.  centre,  with  a  radius  of  3  units,  describe  an  arc  cutting 
the  prolongation  of  N  A  at  B.  Draw  B  E.  From  B,  draw  B  M,& 
l:n<*  '^rpendicular to  the  prolongation  of  HE  at  M,  cutting  the  arc 
first  drawn  at  C,  2  units  distant  from  E.  Draw  C  E.  Draw  b  c  par- 
allel to  B  E  to  represent  the  ray  passing  through  the  prism.  Draw 
e  d  parallel  to  C  E  to  represent  the  emergent  ray. 

In  either  of  these  cases,  the  ratio  between  A  /?and  B  E  is  taken 
equal  to  the  index  of  refraction  for  the  given  media.  The  angles, 
B  E  A  and  B  E  C,  measure  the  deviations  at  the  first  and  second 
refractions  res|>ectively,  while  the  angle,  A  E  C,  measures  the  total 
deviation. 

One  of  these  constructions  may  well  be  giv«>n  to  the  class  as  op- 
tional or  honorary  work,  as  follows  :  Given  E  F  If,  tfafl  s.rtion  of  a 
prism  and  c  d,  thfl  path  of  a  ray  through  tin*  prisni,  to  find  a  method 


250  [Elements  of  Natural  Philosophy,  pp.  507-514.] 

of  determining  the  direction  of  the  incident  and  emergent  rays. 
Give  the  class  a  week  for  the  solution.  If  at  the  end  of  that  time 
any  member  of  the  class  has  succeeded,  have  him  give  his  solution 
to  the  class  and  see  that  he  is  commended  for  his  skill.  If  no  pupil 
succeeds,  the  teacher  may  give  the  solution  and  then  assign  the 
problem  with  the  position  of  the  incident  ray  given,  the  position  of 
the  two  refracted  rays  to  be  determined.  After  the  first  solution  is 
given,  this  will  be  more  easy  and,  during  the  ensuing  week,  some  of 
the  pupils  will  probably  accomplish  it.  See  that  the  constructions 
are  carefully  made,  i.  e.,  that  straight  lines  are  straight ;  that  par- 
allel lines  are  parallel ;  that  equal  lines  are  equal,  etc.  Also,  insist 
upon  neatness. 

See  Frick's  "Physical  Technics/'  p.  192. 

(b.)  A  vessel  for  the  purposes  mentioned  in  the  text 
may  easily  be  made  by  boring  a  hole  through  a  wooden 
prism  and  cementing  pieces  of  window  glass  over  the  ends 
of  the  hole.  The  cavity  thus  made  is  to  be  filled  with 
water  or  other  transparent  liquid  before  cementing  the 
second  plate  in  place. 

§  687.  See  First  Prin.  Nat  Phil,  §  450,  b  and  Picker- 
ing's "  Physical  Manipulation,"  p.  155. 

§  689.  The  focal  distance  of  a  lens  may  be  approximately 
found  by  holding  the  lens  facing  the  window  and  near  a 
wall  on  the  opposite  side  of  the  room.  Move  the  lens 
forward  and  backward  until  the  image  on  the  wall  is  clear. 
Measure  the  distance  from  the  lens  to  the  wall  or  screen. 

§  695.  Measure  the  distances  (D  and  d)  of  the  image 
and  object  from  the  lens  and  the  corresponding  linear 
dimensions  (L  and  I)  of  the  image  and  object.     Verify 

this  formula:  -=-  =  -=-. 
I  a 

§  698.  See  Frick's  "Physical  Technics,"  p.  199. 


[Element*  of  Natural  Philoaoiriy.]  251 

Exercises,  Page  515. 

4.  (a.)  See  §  695.  (b.)  The  image  formed  by  a  concave 
lens  can  not  conform  to  any  of  the  given  conditions.  See 
§697. 

5.  (a.)  See  Fig.  352.  (b.)  12  inches.  (§689,*.)  (c.)  9 
inches. 

6.  (a.)  See  the  lower  part  of  Fig.  356. 

(b.)  See  §  689  (a.)  and  corresponding  note  in  this 
Hand-Book. 

7.  They  will  be  equal.     Construct  the  image.    §  693. 

8.  Eight  inches. 

9.  (a.)  5  feet  from  the  flame.  (§  690.)  Notice  the 
principle  of  reversibility  that  prevails  in  optics.  If  the 
direction  of  an  ether  wave  be  reversed  (the  light  having 
been  reflected  or  refracted  or  not),  the  wave  will  retraverse 
its  original  path  (§  647). 

(b.)  One  will  be  five  times  as  long  as  the  other.  See 
Fig.  358,  and  compare  the  similar  triangles,  ABO,  and 
a  b  0.  The  sides,  a  b  and  A  B,  are  proportional  to  their 
distances  from  0, 


252  [Elements  of  Natural  Philosophy,  pp.  516-520.] 

§  700.  See  Deschanel's  "Natural  Philosophy/'  §  777  and 
Tait's"  Light,"  §§  612,  613. 

"  That  which  we  call  white  light  is,  in  the  state  in  which  we 
receive  it  from  such  a  body  as  a  white-hot  bar  of  iron  or,  perhaps  in 
its  purest  form,  from  the  crater  of  the  positive  pole  of  the  electric 
light  (see  Fig.  247),  a  mixture  of  long  and  short  waves  ;  waves  of  all 
periods  are  either  continuously  present  or,  if  absent  for  a  time,  are 
absent  in  such  feeble  proportions  or  for  such  short  intervals  that 
they  are  not  appreciably  missed  by  the  eye.  White  light  of  this 
kind  is  comparable  to  an  utterly  discordant  chaos  of  sound  of  every 
audible  pitch  ;  such  a  noise  would  produce  no  distinct  impression  of 
pitch  of  any  kind ;  and  so  white  light  is  uncolored." — Daniell. 


§701.  See  Daniell's  "Principles  of  Physics,"  p.  451. 
Concerning  abnormal  dispersion,  see  Tait's  "  Light/' 
§§  196-198. 

§  702.  See  Deschanel's  "Natural  Philosophy,"  §  778. 

§  703.  See  Frick's  "Physical  Technics,"  p.  196;  Desch- 
anel's "  Natural  Philosophy,"  §  779,  with  colored  plate 
(frontispiece)  and  §§  783-790;  Daniell's  "Principles  of 
Physics,"  pp.  449  and  456-460  ;  Tait's  "  Light,"  chap.  XVI, 
and  Hand-Book  note  on  §  722.  The  figure  above  rep- 
resents one  form  of  the  spectroscope. 

§  704.  A   simple  form  of  whirling   table  for  use  with 


[Elements  <:t  Philosophy,  p.  520. \ 


253 


Newton's  Disc  (see  Exp.  2  on  preceding  page  of  text-book) 
is  shown  in  the  accompanying  figure. 
SceTait's  "Light,"  §§  19-21. 

"  The  expression  '  white  light '  standing 
alone  is  wholly  vague ;  physiologically  it 
means  light  which  produces  the  sensation 
of  white  ;  physically  it  may  mean  : — 

"1.  A  mixture  of  all  possihle  light-waves, 
long  and  short,  in  certain  proportions. 

"  2.  A  mixture  of  two  complementary  single 
colors  (§  705,  6). 

"  3.  A  simple  color  blended  with  a  comple 
mentary  compound  one  of  any  degree  of  com- 
plexity. 

"  The  white  light  of  sun-light  at  sea-level  is  made  up  by  a  mixture 
of  colored  lights  in  the  following  proportions  : — Red,  54;  orange-red. 
140;  orange,  80;  orange-yellow,  114;  yellow,  54;  greenish -yellow 
206;  yellowish-green,  121;  green  and  blue-green,  134;  cyan-blue 
32;  blue,  40;  ultramarine  and  blue-violet,  20;  violet,  5." — Daniell. 

§  705.  Most  of  the  colors  seen  in  nature  may  be  imi- 
tated by  mixing  some  prismatic  color  with  white  of  feeble 
intensity.  Each  red  constituent  of  the  spectrum  is  com- 
plementary to  a  constituent  lying  somewhere  in  the 
green.  Each  orange  or  yellow  is  complementary  to  one  of 
the  blues  or  violets.  The  yellowish-greens  are  not  com- 
plementary to  any  single  constituent  of  the  spectrum,  but 
their  complements  may  be  made  by  mixing  red  and  violet 
Lights  (W  pigments). 

Lights  may  be  mixed  by  causing  two  si>ectra  to  overlap  so  that 
at  any  given  point  there  will  be  a  mixture  of  two  colors,  one  from 

each  spectrum.  Also  see  Exp. 
2,  p.  519  of  text-book.  Any 
two  colors  may  thus  be  mixed. 
Another  method  is  by  setting 
a  plate  of  glass,  O,  upright  on 
a  table  with  two  pieces  of  dif- 
ferently colored  papers  on  the 
table  at  equal  distances  from 
A  o        the  glass,  as  at  A  B  and  a  b. 

ZZ  ~L_  '   ■  -■- j^,      When  the  observer  stands  on 


G 


Cx 


B 


254  [Elements  of  Natural  Philosophy,  p.  520!\ 

the  same  side  as  A  B,  he  will  see  a  6  by  light  transmitted  through 
O  and  an  image  of  A  B  formed  by  reflection  by  the  glass.  The 
image  of  A  B  will  coincide  with  a  b  (§  660)  and  the  observer  will  see 
a  mixture  of  the  two  colors.  When  the  eye  is  near  the  plane  of  the 
glass,  as  at  E,  the  image  of  A  B  will  have  the  greater  brightness  ; 
when  it  is  at  e,  the  color  of  a  &  will  predominate.  It  is  easy  thus  to 
vary  the  ratio  in  which  the  colors  are  mixed. 

When  sunlight  passes  through  a  plate  of  colored  glass 
(or  similar  body),  some  of  its  rays  are  absorbed,  becoming 
entangled,  as  it  were,  in  the  glass  and  thus  heating  it. 
Other  rays  find  easy  passage  through  the  glass.  The  char- 
acter of  the  absorption  may  be  determined  best  by  exam- 
ining the  transmitted  light  with  a  spectroscope,  dark  bands 
appearing  in  the  spectrum  in  the  positions  belonging  to 
the  rays  filched  from  the  sunbeam  by  the  glass  plate. 

Common  red  glass  absorbs  nearly  all  except  the  red  rays  ;  cobalt- 
blue  glass  absorbs  the  yellow,  orange  and  scarlet,  and  yields  a 
spectrum  in  which  the  extreme  red  is  separated  by  a  broad  dark 
space  from  the  green,  blue  and  violet. 

V  |  R  G R  (See  §  700,  a.) 

If  two  glass  plates,  one  of  which  thus  absorbs  rays  such  as  the 
other  transmits,  be  superposed4  the  double  plate  will  be  opaque. 
Thus,  red  glass  and  green  glass  are  very  transparent  separately 
viewed,  but  appear  black  when  they  overlap.  On  the  contrary,  red 
light  and  (bluish)  green  light  are  complementary  to  each  other, 
forming  white  light  when  mixed.  A  blue  glass  and  a  yellow  glass 
overlapping,  appear  green,  although  violet  blue  and  yellow  are  com- 
plementary colors  and  such  colored  rays  would  form  a  more  or  less 
perfect  white. 

The  color  of  a  mixture  of  pigments  depends,  like  the 
color  of  superposed  plates,  on  the  composition  of  the  colors 
cf  each  transparent  particle  as  revealed  by  the  spectroscope 
and  not  on  the  apparent  colors  as  seen  by  the  naked  eye. 
See  Tait's  "Light,"  §§  184-189  and  Deschanel's  "Natural 
Philosophy,"  chap.  63. 

"Within  the  limits  of  visibility  (see  Hand-Boob,  note  on  §716) 
there  is  an  indefinite  variety  of  integral  and  fractional  numbers, 
each  of  which  represents  the  frequency  of  a  particular  kind  of  radia* 
tion,  a  particular  kind  of  light.     Physically,  there  are  as  many  kindg 


[MmeMi  "/  Not  oral  Philosophy,  p.  620.]  255 

of  light  as  there  are  possible  frequencies  bcUmon  the  limits  men- 
tioned.  These  kinds  of  light,  each  physically  characterized  by  the 
number  of  waves  which  strike  the  eye  during  a  second,  are  recog- 
nized by  the  eye  as  being  distinct,  not  as  the  result  of  any  conscious 
process  of  counting  the  number  or  impulses  suffered  by  the  eye  dur 
ing  a  second,  which  would  be  absolutely  impossible,  but  in  conse- 
quence of  the  distinct  and  peculiar  sensation  attending  the  reception, 
in  the  eye,  of  wave-motion  of  each  particular  frequency,  a  sensation 
known  in  each  case  as  that  of  a  particular  color.  Thus  when  we 
look  at  a  Bunsen  burner,  the  flame  of  which  is  caused  to  emit  a 
dingy-yellow  light  by  contact  with  common  salt,  we  recognize  the 
sensation  as  one  of  yellow  light.  Color  is  a  sensation  ;  it  is  not  a 
material  existence  ;  but  the  physical  basis  and  cause  of  the  special 
sensation  of  yellow  light  is  in  this  case  the  joint,  simultaneous  im- 
pact on  the  eye  of  two  kinds  of  ether- waves,  which  have  the  respect- 
ive frequencies  of  508,905,810,000,000  and  510,604,000,000,000  per 
second.  Either  of  these  trains  of  waves  impinging  singly  on  the  eye 
would  produce  the  sensation  of  yellow,  the  slower  one  giving  a  yel- 
low very  slightly  more  orange  in  its  tint  than  the  other  does. 

"  The  term  *  yellow  light,'  which  means  primarily  a  certain  sen- 
sation, means  secondarily  the  physical  cause  of  this  sensation — that 
is,  a  train  of  ether-waves  of  a  particular  frequency.  Any  particular 
tolor  is  best  specified  by  a  statement  of  the  frequency  of  the  single 
(rave-motion  which  can  produce  that  color  when  it  enters  the  eye; 
the  analogy  between  light  of  any  given  color  and  a  sound  of  any 
given  pitch  being  obvious. 

"  Even  beyond  the  ordinary  range  of  visibility,  some  eyes  are 
affected  by  ultra-violet  ether-waves  (§717);  a  sensation  of  lavender 
gray  color  results.  A  spectrum  is  often  seen,  especially  if  the 
dispersion  be  small,  to  contain  three  bright  bands  of  lavender-gray 
in  the  ultra-violet  region. 

"  The  color  of  a  colored  object,  as  seen  by  transmitted  light,  is 
produced  by  subtraction  of  the  light  absorbed  from  the  light  Inci- 
dent upon  the  object.  The  kind  of  light  transmitted  may  vary  with 
the  thickness  of  the  absorbing  medium.  A  solution  of  chloride  of 
chromium  in  a  thin  layer,  absorbs  much  yellow,  orange  and  yel- 
lowish-green light ;  in  a  thicker  layer,  it  absorbs  all  but  the  red 
and  some  green  and  blue;  in  a  still  thicker  layer,  the  only  <« »1«  r  - 
transmitted  is  red.  Thus  a  wedgc-shajH-d  layer  of  this  solution  ap 
pears  to  vary  in  color,  according  to  tin*  thickness,  from  a  greenish- 
blue,  through  purple,  to  red.  Iodine  vai>or  transmits  a  blue  group 
and  a  red  group,  as  also  ultra-violet  rays;  together  these  produce  an 
impression  of  purple  ;  in  thicker  layers,  the  blue  rays  alone  are 


256  [Elements  of  Natural  Philosophy,  p.  520 .] 

transmitted  and  the  vapor  appears  blue.  When  a  strong  solution 
of  blood  is  interposed  in  the  path  of  a  beam  of  light,  no  light  but 
red  is  transmitted  ;  dilute  the  solution  gradually  and  successively, 
the  solution  appears  more  and  more  yellowish  and  of  increasingly 
paler  hue. 

"  The  special  absorptions  of  absorbent  bodies  are  most  thoroughly 
studied,  not  by  means  of  their  visible  colors,  but  by  the  prismatic 
analysis  of  the  light  which  passes  through  them.  It  is  then  found 
that  some  substances  absorb  several  distinct  kinds  of  light,  belong- 
ing to  different  regions  of  the  spectrum.  Transparent  colored 
objects,  through  which  light  is  filtered,  give  dark  bands  across  the 
spectrum— the  so-called  Absorption  bands  which  indicate  what  kind 
of  light  has  been  stopped  and  extinguished  by  the  absorbent  object — 
these  bands  varying  in  breadth  with  the  degree  of  concentration  of 
the  absorbent  solution  employed  and  varying  in  position  with  its 
nature.     (See  §  625  and  note.) 

"  The  color  of  a  colored  object  seen  by  reflected  light  is  also  gen- 
erally due  to  absorption.  An  object  seen  by  reflected  sunlight  does 
not  seem  to  be  colored  in  any  degree  unless  there  have  been  abscrp 
tion  of  some  of  the  components  of  the  incident  white  light ;  th? 
color  of  a  colored  object  is  complementary  to  the  color  that  would 
have  been  produced  by  these  absorbed  components  had  they  jointly 
impinged  on  the  eye. 

"  Some  of  the  light  incident  on  a  piece  of  colored  glass  is  reflected 
at  its  surface  ;  there  is  no  absorption  ;  if  the  incident  light  be  white, 
the  light  reflected  is  also  white.  If  a  piece  of  green  glass  be  laid 
upon  black  paper,  and  if  it  be  looked  at  in  such  a  direction  that  day- 
light is  not  directly  reflected  from  it  into  the  eye,  it  will  be  nearly 
invisible  and  will  be  devoid  of  color  ;  it  will  appear  black.  If  col- 
ored glass  be  ground  to  powder,  the  powder  is  white  ;  white  light  is 
reflected  at  every  facet  while  the  light  reflected  from  the  lower  sur- 
faces of  the  fragments  and  again  issuing  into  the  air  has  nowhere 
traversed  a  layer  of  sufficient  thickness  to  cause  the  extinction  of  all 
the  absorbable  components  of  the  incident  sunlight.  The  finer  the 
powder,  the  whiter  it  is ;  the  coarser  it  is  the  more  marked  is  its 
color.  If  the  upper  surface  of  a  sheet  of  green  glass  be  ground,  it 
will  appear  almost  white  ;  if  the  ground  surface  be  looked  at  through 
the  glass,  it  will  appear  green,  for  the  light  issuing  from  the  glass 
is  white  light  which  has  undergone  a  certain  amount  of  absorption. 
If  the  green  powder  be  immersed  in  water  or  oil,  there  is  less  reflec- 
tion at  the  several  facets ;  there  is  deeper  penetration  of  the  light 
into  the  mass  and,  consequently,  more  absorption  ;  the  color  appears 
to  deepen.     Hence  the  value  of  oil  as  a  medium  in  painting. 


[Elements  of  Natural  Philosophy,  p.  520.]  257 

"  A  solution  of  chloride  of  copper  placed  in  a  deep  black-walled 
vessel  will  not  appear  to  have  any  color  ;  it  will  seem  black ;  it  re- 
flects no  light  except  from  its  surface.  If  powdered  chalk  be  mixed 
with  it,  light  is  reflected  from  the  white  particles  of  chalk  and 
passes  out  in  every  direction,  through  every  part  of  the  surface  ;  so 
much  of  the  reflected  light  is  absorbed  that  it  appears  green  when 
it  reaches  the  eya — the  milky  mats  appears  green.  In  a  similar 
way,  a  piece  of  malachite  is  penetrated  by  light  to  a  very  small 
depth ;  internal  reflection  occurs ;  absorption  of  all  the  outpassing 
light  takes  place  with  the  exception  of  certain  kinds  which  jointly 
ap|iear  green  ;  the  malachite  is  green.  A  piece  of  polished  gold 
reflects  white  light  at  its  surface  ;  it  also  reflects  interiorly  and  from 
within  the  substance  of  the  gold  at  a  very  small  depth  there  is  re- 
flected in  all  directions  a  quantity  of  light  which,  by  absorption 
before  leaving  the  surface,  has  become  of  an  orange  color.  If  the 
layer  of  gold  be  very  thin,  that  part  of  the  light  which  would  be 
absorbed  by  a  thicker  layer  may,  in  part,  pass  through  and  issue 
into  transparent  media  before  its  energy  is  wholly  converted  into 
heat.  A  thin  piece  of  goldleaf  thus  appears  transparent  and  allows 
a  greenish-blue  kind  of  light  to  pass  through  it,  which,  if  the  leaf 
be  rendered  very  thin  by  the  action  upon  it  of  a  solution  of  cyanide 
of  potassium,  may  become  violet,  for  both  green  and  violet  light 
then  find  their  way  through. 

■  Greenish-blue  glass  prevents,  in  whole  or  in  part,  the  transmis- 
sion of  violet  light,  of  red,  of  orange  and  of  other  kinds  of  light 
that  are  present  in  white  sunlight.  The  complex  of  undulations 
thus  denied  transmission  would,  if  collectively  allowed  to  impinge 
on  the  eye,  have  produced  a  single  impression  of  red  light.  If  this 
compound  red-light  had  not  been  obstructed  by  the  colored  glass,  the 
transmitted  beam  would  have  been  white  ;  this  compound  red-light 
thus  obstructed  by  the  greenish  glass,  and  the  compound  greenish- 
light  transmitted  by  it,  will  pass  together  through  a  piece  of  char 
glass  and  will  together  produce  the  sensation  of  white  light.  To 
the  eye  it  is  a  matter  of  indifference  whether  the  red  or  the  greenish 
light  lie  monochromatic  or  compound  ;  monochromatic  red-light  and 
monochromatic  greenish  blue-light,  allowed  to  fall  upon  the  same 
spot  in  the  eye  will  mingle  and,  if  they  be  of  the  proper  tint,  will 
produce  the  compound  sensation  of  white  light.  These  colors,  red 
and  greenish -blue,  each  of  the  proper  tint,  are  thus  complementary 
to  one  another  ;  together,  they  make  up  white  light. 

'The  following  pairs  of  colors  are,  among  others,  thus  comple- 
mentary to  ope  another  :  red  and  a  very  greenish-blue  ;  orange  and 
cyan-blue  (a  rather  greenish-blue) ;    yellow  and  ultramarine  blue ; 


258  {Elements  of  Natural  Philosophy,  pp.  620-525.] 

greenisli-yellow  and  violet ;  green  and  '  purple,'  the  latter  being  a 
color  not  in  the  spectrum  but  formed  by  the  superposition  of  blue 
and  red." — Daniell. 

§  706.  See  Tait's  "Light,"  chap.  x.  and  Frick's  "Phys- 
ical Technics,"  p.  197  (§  168). 

"  Fill  a  glass  bulb  about  1£  inches  in  diameter  (those  furnished 
for  air-thermometers  answer  the  purpose)  with  a  filtered  solution  of 
common  salt  in  water.  Cover  the  aperture  of  the  porte-lumiere 
(heliostat)  with  a  black  cardboard  so  as  completely  to  exclude  the 
light  from  a  darkened  room.  Cut  a  hole  in  the  centre  of  the  card- 
board of  the  same  diameter  as  the  bulb  and  allow  a  circular  beam 
of  light  to  pass  through  it  and  also  through  a  hole  of  about  4  in. 
diameter  in  the  centre  of  a  white  cardboard  about  2  ft.  square  and 
strike  the  bulb  placed  at  a  distance  of  about  2  ft.  in  front  of  the  white 
cardboard.  A  miniature  rainbow  will  be  reflected  back  from  the 
bulb  upon  the  screen  around  its  aperture.  Any  spot  on  the  screen 
where  red  appears  means  that  an  eye  situated  at  that  point  would  see 
red  in  the  glass  bulb.  Every  other  color,  unless  the  eye  was  moved, 
would  require  another  bulb  in  the  proper  relative  position." — Gage. 

§  711.  See  Frick's  "Physical  Technics,"  p.  198  (§  169). 

§  712.  "  The  imperfection  of  the  achromatism  of  the  eye  is  readily 
proved  by  looking  through  a  plate  of  cobalt  glass  at  a  small  hole  in 
the  shutter  of  a  dark  room.  The  hole  at  first  appears  red  with  a 
blue  space  around  it ;  but,  by  an  effort  of  the  muscles  of  the  eye,  we 
can  see  the  hole  blue,  and  then  there  is  a  red  space  surrounding  it. 
Rays  of  so  widely  different  refractive  index  cannot  be  seen  in  focus 
simultaneously."—  Tait. 

§  713.  See  Tait's  "Light," chap,  xiv.;  Pickering's  "Phys- 
ical Manipulation,"  p.  199;  Stokes's  "Nature  of  Light," 
Lecture  II;  Frick's  "Physical  Technics,"  p.  219  (§  189) 
and  Daniell's  "  Principles  of  Physics,"  p.  501.  If  rays  of 
red  light  fall  perpendicularly  upon  the  flat  surface  of  a 
plano-convex  lens  of  several  feet  focal  length,  the  convex 
surface  being  pressed  against  the  plane  surface  beneath  at 
a,  a  black  spot  will  appear  at  a  and  black  rings  at  w,  x,  y 
and  z. 

The  centre  is  black  because  the  waves  reflected  from  the  two  sur- 
faces in  contact  at  a  meet  in  opposite  phases.  They  meet  in  opposite 
phases  because  the  wave  reflected  from  the  rarer  medium   changes 


{Elements  of  Natural  Philosophy,  pp.  6*6-698.]  25$ 


C 

V 

\ 

\ 

V 

\ 

\ 

Z m \z 

l^>^^w  -J2^^" 

a  h       C    d   e 


(It  phase  or  logos  a  lialf  wave  length  while  the  wave  reflected 
from  the  denser  medium 
does  not.  The  fintf  dark 
ring  shows  that  tin-  waves 
reflected  from  b  interfere 
with  those  reflected  Cram  ». 
Tin1  waves  reflected  from  6 
inns'  travel  one  red  wave 
length  furtln-rtlianthr  wav.  s 
dfrom  w.  That  is,  //  m 
equals  half  a  red  wave 
length!  1m  similar  manner, 
we  see  that  c  x  equals  a  wave 
length  ;  d  y,  a  wave  length 
and  a  half ;  e  z,  two  wave 
lengths.  The  diameter  of 
the  fourth  dark  ring,  z  z'  or 
2  in  2  may  be  found  by  nnas 
urement.  The  radius  of 
curvature,  C  z,  may  also  be  measured.  C  m  z  is  a  right-angled 
triangle  with  the  two  sides,  Cz  and  tti  z,  found  by  direct  measure  - 
ment.  Hence,  we  can  easily  determine  the  value  of  C  m.  Ca  =  Cz. 
Then  Ca  —  Cm  =  am  —  ez  =  2  wave  lengths  of  red  light. 

The  twinkling  of  stars  is  an  effect  of  interference.  See 
haniell's  '*  Principles  of  Physics,"  p.  508. 

§  714.  See  Frick's  u  Physical  Technics,"  p.  222  (§§  191- 
193);  Tait's  "  Light,"  §§  235-242;  Pickering's  "  Physical 
Manipulation,"  p.  202;  Deschanel's  "  Natural  Philosophy," 
p.  1024  et  seq.y  and  Danicll's  "  Principles  of  Physics,"  p.  50C. 

§  716.  All  known  ether  waves  vary  from  about  107  > 
to  about  4  x  1016  vibrations  per  second.  There  may.  of 
course,  be  ether-waves  t hat  have  a  frequency  of  vibration 
lian  tlic  first  of  these  numbers  and  others  that  haves 
frequency  greater  than  the  number  last  given,  but  we  are 
not  provided  with  senses  that  can  recognize  them  if  they 
do  exist  and,  at  present,  have  no  experimental  means  of 
investigating  them  even  if  they  are  awaiting  investigation. 
(See  Hand-Book  note  on  Jj  496.)  But  the  limits  above 
indicated  cover  what    we  may  tall  a  range  of  about  eight 


260  [Mements  of  Natural  Philosophy,  pp.  528,  529] 

and  a  half  octaves.  But  the  human  eye  has  a  range  of  only 
about  a  single  octave,  being  sensitive  to  vibrations  ranging 
from  about  392  x  1012,  per  second,  a  frequency  that  gives  rise 
to  the  sensation  of  the  extreme  red  of  the  spectrum,  to 
about  75?  x  1012,  a  frequency  that  occasions  the  sensatioL 
of  violet  at  the  other  end  of  the  spectrum.  These  wave- 
lengths are  sometimes  measured  in  "tenth-meters,"  which 
name  is  given  to  1  meter  -f-  1010  =  0.0000000001  m.  = 
0.00000001  cm.     See  Tait's  "  Light,"  §  231. 

§  717.  The  length  of  luminous  waves  is  most  accurately 
measured  by  diffraction  spectra.  See  Deschanel's  "  Natural 
Philosophy,"  §§  821,  822.  The  use  of  Newton's  Rings  for 
this  purpose  was  explained  on  p.  259  of  this  Hand-Book. 

"  Ether  waves  do  Dot  traverse  all  substances  with  equal  speed 
hence  their  wave-lengths  in  different  substances  vary.     If  any  par 
ticular  kind  of  radiation  have  to  be  spoken  of,  it  may  be  denned  by 
specifying  its  wave-length  in  some  specified  medium,  but  it  is  better 
to  state  its  numerical  frequency." — Daniell. 

§  718.  All  of  the  various  rays  that  constitute  a  sunbeam, 
i.e.,  ether-waves  of  all  known  lengths,  are  thermal  rays,  for 
their  energy  is  convertible  into  heat  when  they  fall  upon  a 
thick  layer  of  lamp-black  which  absorbs  most  of  them.  If 
the  frequency  of  the  waves  is  less  than  392,000,000,000,000 
(=r  392  x  1012)  per  second,  the  wave  is  too  long  and  too 
slow  to  cause  vision  or,  as  a  general  thing,  to  agitate  the 
molecules  upon  which  they  strike,  with  a  motion  brisk 
enough  to  shake  them  to  pieces  and  thus  to  work  chemical 
decomposition.  The  energy  of  such  waves  is  convertible 
only  into  sensible  heat;  they  are  dark-heat  waves.  "If 
they  fall  upon  an  ordinary  photographic  plate  they  do  not 
produce  chemical  decomposition  ;  but  if  the  molecules  upon 
which  they  impinge  be  specially  heavy  and  complex,  even 
these  slow  heat-waves  may  be  found  to  toss  and  shake 
them  with  briskness  sufficient  to  break  them  up." 

§  719.  See  Frick's  "Physical  Technics,"  p.  200. 

Ether  waves  with  a  frequency  greater  than  757  x  10" 


[Elements  of  Natural  Philosophy,  p.  5  :•.  ]  861 

per  second  are  s?  rapid  that  the  human  eye  is  unable  to 
!<d  to  their  impact  :  it   is  blind  to  tbem.    But  such 
ultra-violet  rays  may  effect  cbemical  decomposition. 

"  Their  rocWBhne  impulses  may  aid  the  natural  free  vibrations  of 
tin-  molecule  which  thus  become  increasingly  ample.  Just  as  I 
nant  tumbler  into  Which  its  own  note  is  steadily  sung,  vibratos, 
shivers  and  breaks  into  fragments,  so  a  molecule,  quivering  under 
the  steady,  regular  and  continuously  well-timed  blows  of  the  rapid 
'tlur-waves,  may  yield  and  break  up  into  its  constituent  atoms,  or 
into  groups  of  atoms  which  constitute  simpler  molecules. 

"  The  ultra-violet  part  of  the  solar  spectrum  is  comparatively  very 
short  on  account  of  absorption  (of  actinic  rays)  by  the  atmosphere. 
This  effect  of  the  atmosphere  is  of  extreme  importance.  Sunlight 
is  originally  bright  blue  and  is  extremely  rich  in  the  more  refrangi- 
ble rays.  But  filtration  through  two  absorbent  atmospheres  (that  of 
the  sun  and  that  of  the  earth)  renders  it  a  yellowish  white.  The 
ultra-violet  part  of  the  spectrum  is  enormously  brighter  at  high 
altitudes. 

"Makers  of  photographic  lenses  have  shown  much  skill  in 
making  the  photographic  and  the  visual  focus  coincide.  For  special 
photographic  work,  lenses  have  had  to  be  constructed  whose  curva- 
ture is  calculated  with  reference  to  the  focus  of  the  highly  refrangi- 
ble actinic  rays  alone  ;  while  nothing  can  be  distinctly  seen  through 
wch  lenses,  photographs  of  extraordinary  clearness  have  been  taken 
by  their  aid." — Daniell. 

A  decoction  of  the  bark  of  the  horse  chestnut  is  easily 
obtained  and  "  powerfully  fluorescent."  The  fluorescence 
may  be  exhibited  by  exposing  a  glass  of  the  liquid  to  the 
electric  light  See  §  720  and  the  Hand-Book  note  thereon. 
A  good  substitute  for  the  electric  light  may  be  provided 
by  burning  magnesium  wire  or  ribbon.  The  magnesium 
light  is  rich  in  actinic  rays.     See  Elem.  Chcm.,  g  298. 

\\V  have  seen  that  ether-waves  may  penetrate  to  the 
interior  particles  of  a  body  upon  which  the  waves  fall. 
These  interior  particles  may  reflect  waves  of  such  frequency 
as  to  constitute  luminous  rays.  Such  a  body  tfl  then 
fluorescent.  In  other  cases,  the  molecules  continue  t  • 
vibrate  for  some  time  after  ether-waves  have  ceased  to  fall 
upon  the  body  which  the  molecules  constitute.     Just  as  a 


262  [Elements  of  Natural  Philosophy,  pp.  529-531] 

bell  continues  to  vibrate  after  the  blows  of  the  hammer 
have  ceased,  and  sends  out  sonorous  air-waves,  so  the 
vibrating  molecules  continue  to  radiate  ether-waves.  We 
are  very  familiar  with  the  phenomenon  when  the  ether- 
waves  are  so  slow  as  to  constitute  heat-rays.  When,  how- 
ever, the  ether-waves  thus  produced  are  of  such  a  frequency 
as  to  constitute  luminous  rays,  we  say  that  the  body  isphos* 
phorescent.  Phosphorescent  "luminous  paint"  is  now  in 
somewhat  common  use.  See  Stokes's  "  Light  as  a  Means 
of  Investigation,"  Lecture  I;  Daniell's  "Principles  of 
Physics,"  p.  467  and  Taifs  "Light,"  §§  76  ;  199-204. 

"The  view  which  I  have  all  along  maintained  is  that  the  incident 
vibrations  caused  an  agitation  among  the  ultimate  molecules  of  the 
body  and  that  these  acted  as  centres  of  disturbance  to  the  surround- 
ing ether,  the  disturbance  lasting  for  a  time  which,  whether  it  was 
long  enough  to  be  rendered  sensible  in  observation  or  not,  was  at 
any  rate  very  long  compared  with  the  time  of  a  luminous  vibration. 
And  now  that  M.  E.  Becquerel  has  shown  experimentally  by  his 
beautiful  phosphoroscope  the  finiteness  of  duration  of  the  emission 
of  light  in  the  case  of  solids  in  which  it  was  so  brief  that  its  emis- 
sion was  described  as  '  fluorescence,'  as  in  a  solution  of  a  sulphate 
of  quinine,  there  can  no  longer  be  any  doubt  as  to  the  identity  of 
nature  of  phosphorescence  and  fluorescence,  even  though  the  finite 
duration  of  the  emission  of  light  after  the  incident  rays  have  been 
cut  off  has  not  at  present  been  experimentally  demonstrated  in  the 
case  of  any  liquid." — Stokes. 

§  720.  As  stated  in  the  note  on  §  719,  the  ultra-violet 
part  of  the  solar  spectrum  is  much  shortened  by  absorp- 
tion by  two  atmospheres.  But  if  the  light  of  an  electric 
arc  be  analyzed  with  a  quartz  prism,  the  ultra-violet  part 
of  the  spectrum  is  six  or  seven  times  as  long  as  the  colored 
part.  A  glass  prism  absorbs  these  waves  of  great  fre- 
quency, or  of  high  refrangibility,  to  a  remarkable  extent. 

§  721.  A  good  analogy  is  found  in  acoustics.  A  musical 
string  or  a  resonator  (§§  509,  514)  can  rob  the  air  of  some 
of  the  energy  of  certain  sounds  and  thus  be  set  in  vibra- 
tion. When  they  themselves  are  set  in  vibration,  thus  or 
otherwise,  they  reproduce  sounds  of  the  same  tone  as 
those  that  they  absorbed  from  the  air. 


\  Elements  of  Natural  Philosophy,  p.  5S1.\  263 

§  722.  A  piece  of  platinum  may  be  placed  at  the  focus 
of  a  rock-salt  lens  and  heated  intensely  by  dark-heat  rays 
converged  by  the  lens.  The  radiation  of  the  calorescent 
platinum  will  include  ether-waves  of  all  kinds;  if  the 
emitted  rays  be  examined  by  a  prism,  they  will  g\w  a 
continuous  spectrum,  showing  that  waves  of  all  degrees  of 
ivt'rangibility  (i.  e.,  of  all  kinds  of  wave-length  and  all 
kinds  of  rate  of  vibration,  within  the  limits  of  its  spectrum ; 
are  present.  But  the  molecules  of  some  substances  seem 
to  be  tuned  to  particular  rates  of  vibration ;  such  mole- 
cules will  absorb  the  energy  of  vibrations  of  their  own 
frequencies.  A  body  composed  of  such  molecules  will  be 
athemanous  or  opaque  to  such  rays. 

■  If  a  screen  of  strings  tuned,  say  to  the  note  of  a,  be  arranged 
between  a  sounding  a  organ-pipe  and  a  listener,  the  latter  will  hear 
comparatively  little  of  the  sound  produced  by  the  pipe;  by  resonance,  • 
the  strings  have  taken  up  the  energy  and  have  converted  part  of  it 
into  heat.  If  a  mixed,  sound  were  produced  on  the  farther  side  ot 
such  a  screen,  the  sound  of  a  would  not  be  transmitted  to  such  a 
listener  ;  the  rest  of  the  mixed  sound  would  be  heard  by  him. 

*'  From  the  reciprocity  of  absorption  and  radiation  it  follows  that 
if  a  given  substance  be  divided  into  portions  of  which  the  one,  A, 
is  hot  while  the  other,  B,  is  comparatively  cool,  radiations  from  ,  I 
will  be  absorbed  by  B ;  the  cooler  portion,  B,  is  opaque  to  radiations 
from  the  hotter  portion,  A.  Thus,  if  carbonic  oxide  be  burned,  its 
flame  contains  hot  carbonic  acid  (C02);  the  radiations  from  such  a 
flame  cannot  pass  through  pure  CO,  and  are  checked  in  very  large 
proportion  by  air  containing  even  a  very  small  percentage  of  that 
gas.  A  hydrogen  flame  contains  hot  aqueous  vapor ;  the  heat 
radiated  from  this  (very  slow,  dark -heat  waves)  cannot  pass  through 
aqueous  vapor.  In  this  way,  as  Prof.  Tyndall  has  shown,  while  the 
sun's  light  and  heat  can  reach  the  earth's  surface  through  the  humid 
atmosphere,  their  effect  is  to  warm  the  earth  and  cause  it  to  produce 
slow  waves  of  dark  heat  ;  these  resemble  in  frequency  the  waves 
produced  by  hot  aqueous  vapor  in  a  hydrogen  flame  and  they  cannot 
pass  away  through  the  aqueous  vapor  of  the  atmosphere.  The 
atmosphere  thus  acts  as  a  kind  of  heat  trap  and  the  surface  of  the 
earth  is  preserved  from  extremes  of  cold  produced  by  excessive  radia- 
tion. But  for  the  atmosphere,  the  earth's  temperature  would  be  belo* 
—  45°  C„  even  under  the  vertical  rays  of  a  tropical  sun." — Darnell 


264  [Elements  of  Natural  Philosophy,  pp.  533-540.] 


Exercises,  Page  533, 

2.  188,000  x  5,280  x  12  x  50,000  =  595,584,000,000,000. 
— Am. 

§  724.  See  Prick's  "Physical  Technics,"  p.  201  (§  172). 

§  725.  See  Frick's  "Physical  Technics,"  p.  205  (§§  175, 
L76,  .178);  Tait's  "Light,"  §§  13-18,  22,  23  and  Daniell's 
"  Principles  of  Physics,"  p.  528. 

§  727.  For  methods  of  testing  the  eye,  see  Pickering's 
"  Physical  Manipulation,"  p.  191. 

§  729.  One  of  the  many  forms  of  the  compound  micro- 
scope, with  stand,  stage,  reflector, 
etc.,  is  shown  in  the  accompanying 
figure.  See  Frick's  ' '  Physical  Tech  - 
nics,"  p.  210  (§§  182-185) ;  Picker- 
ing's "Physical  Manipulation,"  pp. 
156-174  and  Deschanel's  "  Natural 
Philosophy,"  §  751. 

§  731.  The  great  refractor  at  the 
Pulkova  (Kussia)  Observatory  has 
a  30-inch  objective.  The  great 
lenses  of  both  this  and  the  Lick 
telescopes  were  ground  and  polished 
by  the  Olarks  of  Cambridge,  Mass. 
In  1886,  Mr.  Alvan  Clark  received 
from  the  Kussian  Minister  at  Wash- 
ington a  gold  medal  awarded  him  by  the  Czar.  It  is  said 
that  only  two  establishments  in  the  world  can  cast  the  glass 
discs  for  such  great  lenses.  One  of  these  is  in  France ; 
the  other,  in  England.  When  the  Feils  of  Paris,  after 
many  failures,  succeeded  in  making  the  crown  glass  disc 
for  the  Lick  Observatory  telescope,  they  made  two  discs. 
The  second  disc  was  secured  for  the  Lick  Observatory  to 
be  finished  as  a  photographic  corrector  for  the  telescope- 
See  Hand-Book  note  on  §  719.     Within  the  last  few  years, 


[Elements  of  Natural  Philosophy,  pp.  540,  541.]         265 

astronomical  photography  has  become  of  immense  impor- 
tance in  the  scientific  study  of  the  heavens. 

§  733.  In  telescopes  used  for  making  observations 
of  direction,  very  fine  threads,  called  cross-wires  or  cross- 
I,  are  made  to  intersect  at  the  common  focus  of  the 
object  glass  and  eye  piece.  Their  intersection  is  appar- 
ent ly  at  the  same  place  as  the  distant  objects.  Spiders' 
threads  are  generally  used  by  surveyors  for  this  purpose. 
Cross-hairs  are  necessary  for  directing  the  line  of  sight 
to  the  precise  point  to  be  observed,  since  a  considerable 
field  of  view  is  seen  in  looking  through  the  telescope. 

Sir  John  Herschei  says  :  "  This  application  of  the  telescope  may 
be  considered  as  completely  annihilating  that  part  of  the  error  of 
observation  which  might  otherwise  arise  from  an  erroneous  estima- 
tion of  the  direction  in  which  an  object  lies  from  the  observer's  eye 
or  from  the  centre  of  the  instrument.  It  is,  in  fact,  the  grand  source 
of  all  the  precision  of  modem  astronomy,  without  which  all  other 
refinements  in  instrumental  workmanship  would  be  thrown  away." 
These  remarks  apply  equally  well  to  surveying. 

"  The  brightness  of  the  image  seen  in  a  telescope  or  microscope 
can  never  exceed  the  brightness  of  the  object  as  seen  by  the  naked 
eye  except  in  the  case  of  bodies  which,  like  stars,  appear  mere  lumi- 
nous points.  In  the  majority  of  cases  there  is  great  loss  of  bright- 
ness as  compared  with  that  presented  to  the  naked  eye.  When  a 
telescope  or  microscope  is  directed  toward  the  sky,  a  real  image  of 
the  objective  is  formed  by  the  ocular  and  may  be  received  on  a  piece 
of  thin  paper  held  |  or  \  inch  behind  the  ocular.  If  this  bright  spot 
on  the  paper  is  smaller  than  the  pupil  of  the  observer's  eye,  the 
difference  represents  so  much  loss  of  brightness.  If  it  is  larger  than 
the  pupil,  there  is  no  gain  of  light  because  the  light  that  falls  outside 
the  pupil  (when  the  pupil  is  put  in  the  place  of  the  spot  on  the  paper) 
does  not  contribute  to  vision.  In  telescopes,  the  diameter  of  the 
objective  divided  by  the  diameter  of  this  spot  is  equal  to  the  magni- 
fying power.  A  large  objective,  therefore,  permits  a  high  magnify- 
ing power  to  be  used  without  rendering  the  bright  spot  smaller  than 
the  pupil."— Everett. 

But,  at  the  best,  there  is  a  loss  of  brightness,  because 
lenses  transmit  and  specula  reflect  only  a  part  of  the 
incident  light. 


266         [^Elements  of  Natural  Philosophy,  pp.  542-547.] 

§  734.  Be  sure  to  get  Prof.  Dolbear's  "  Art  of  Project- 
ing." Slides  for  the  magic  lantern  or  heliostat  may  be 
made  by  smoking  (in  a  kerosene  flame)  pieces  of  glass  of 
suitable  size  and  tracing  thereon  the  design  wanted.  These 
plates  may  be  made  in  a  form  more  convenient  by  painting, 
instead  of  smoking,  them.  Use  a  paint  made  by  mixing 
venetian-red  with  water  to  which  a  little  gum  arabic  has 
been  added  and  apply  evenly  with  a  broad,  flat  brush. 

§  736.  See  Frick's  "Physical  Technics,"  p.  209  (§  180). 

§  737.  The  polarizer  and  analyzer  together  constitute  a 
polariscope.  Some  writers,  with  etymological  accuracy, 
speak  of  the  second  instrument  alone  as  a  polariscope. 

"  There  are  individuals,  generally  with  very  dark  eyes,  who  are 
able  to  distinguish  polarized  light  from  common  light,  because  of  a 
polarizing  structure  in  the  eye  itself.  This  gives  rise  to  what  are 
called  Haidinger's  Brushes,  whenever  polarized  light  falls  on  the 
eye.  Such  individuals  see  the  brushes  in  all  reflected  or  refracted 
(i.  e.,  partially  polarized)  light.  The  great  majority  of  men,  how- 
ever, can  only  see  the  phenomenon  with  polarized  light  and  then 
with  difficulty.  The  best  way  of  making  the  observation  is  to  look 
through  a  Nicol  at  a  bright  cloud  or  a  piece  of  white  paper  well 
illuminated  and  to  give  a  slight  rotation  to  the  Nicol  at  intervals. 
In  the  line  of  sight  there  will  be  detected  four  little  colored  tufts  or 
brushes,  two  having  a  brownish,  the  others  a  bluish  or  purplish 
tint." — Tait. 

See  Frick's  "Physical  Technics,"  p.  225  (§§  194-199); 
Stokes's  "Nature  of  Light,"  p.  90  et  seq.;  Pickering's 
"Physical  Manipulation,"  pp.  208-225;  Tait's  "Light," 
chap.  xv.  and  Daniell's  "  Principles  of  Physics,"  pp.  476- 
479. 

§  741.  Many  substances  divide  an  incident  beam  of 
light,  reflecting  some  of  the  rays  and  refracting  others 
(§  676).  With  such  substances,  it  has  been  found  that  the 
angle  of  incidence  coincides  with  the  angle  of  polarization 
when  the  reflected  and  the  refracted  rays  are  at  right  angles 
to  each  other.     This  may  be  shown  with  the  apparatus  men- 


[Element*  of  Natural  PhU»*,yhy>   ,  >.]  2W 


tioned  in  the  note  on  £  679  (page  24,  of  this  Band-Book). 
By  means  of  the  movable  mirror,  the  incident  beam  may 
be  thrown  in  any  desired  direction.  By  rendering  the 
water  slightly  turbid  with  milk  and  throwing  a  little  smoke 
into  the  space  above  the  water,  the  paths  of  the  incident, 
reflected  and  refracted  beams  will  all  be  made  visible.  By 
adjusting  the  mirror  so  that  the  reflected  beam  makes  an 
angle  of  90°  with  the  refracted  beam,  both  the  reflected 
and  the  refracted  light  will  be  polarized,  the  plane  of 
vibration  in  one  beam  being  perpendicular  to  the  plane  of 
vibration  in  the  other,  as  may  be  shown  by  examination 
with  a  tourmaline  analyzer  or  with  a  Nicol's  prism.  (See 
§  744.)  If  such  an  analyzer  be  placed  in  the  path  of  the 
incident  beam  (the  incident  beam  being  thus  polarized), 
and  then  turned  about  its  axis,  the  intensity  of  the  re- 
flected and  the  refracted  beams  will  alternate  between 
maximum  and  minimum.  By  such  means,  the  polarizing 
angle  of  any  liquid  is  easily  ascertained. 

The  law  may  be  expressed  as  follows : 

The  tangent  of  the  polarizing  an- 
gle is  equal  to  the  refractive  index 
(§  678)  of  the  reflecting  substance, 
— or 


mien  the  reflected   ray    is   com- 
pletely polarized,  it  is  perpendicular 
to  the  refracted  ray. 

§743.  See  Frick's  "Physical  Tech- 
nics," p.  233  (§§  200-212)  and  Daniells 
"  Principles  of  Physics,"  p.  509. 

§  744.  The  accompanying  cut  shows 
the  position  of  the  bisecting  plane  rela- 
tive to  the  ends  of  the  prism.  It  is 
evident  that  two  Nicols,  placed  in  proper 
position,  constitute  a  complete  polari- 
scope.    When  placed  so  that  the  analyzer 


268  [Elements  of  Natural  Philosophy,  p.  54$.] 

quenches  the  light  transmitted  by  the  polarizer,  the  prisms 
are  said  to  be  "  crossed."     See  "■Nature,"  Vol.  35,  p.  184. 

"  By  far  the  most  perfect  polarizer  for  a  broad  beam  of  light  is  a 
crystal  of  Iceland  spar  sufficiently  thick  to  allow  of  the  complete 
separation  of  the  two  rays.  But  such  specimens  are  rare  and  costly, 
so  that  the  polarizer  in  practical  use  is  now  what  is  called  NicolCs 
prism,  invented  in  1828." — Tait. 

If  on  a  clear,  bright  day,  we  examine  the  blue  sky  with 
a  Nicol,  we  shall  find  traces  of  polarization  in  many  direc- 
tions, but  the  effect  will  be  most  noticeable  in  directions 
at  right  angles  to  a  line  from  the  sun  through  the  eye  of 
the  observer,  i.  e.,  when  we  are  looking  across  the  direction 
of  the  solar  rays.  When  the  sun  is  in  the  horizon  (rising 
or  setting),  the  best  effect  is  produced  by  looking  through 
the  Nicol  at  some  point  of  the  sky  that  lies  in  a  circle 
drawn  through  the  zenith,  the  north  and  the  south  points. 
When  the  sun  is  in  the  zenith,  the  best  results  will  be 
found  by  looking  toward  the  horizon.     Mr.  Tyndall  says: 

"  The  sun  was  near  setting  and  a  few  scattered  neutral-tint  clouds, 
which  failed  to  catch  the  dying  light,  were  floating  in  the  air.  When 
these  were  looked  at  across  the  track  of  the  solar  beams,  it  was 
possible,  by  turning  the  Nicol  round,  to  see  them  either  as  white 
clouds  on  a  dark  ground,  or  as  dark  clouds  on  a  bright  ground. 
In  certain  positions  of  the  prisms,  the  sky -light  was  in  great  part 
quenched,  and  then  the  clouds,  projected  against  the  darkness  of 
space,  appeared  white.  Turning  the  Nicol  90°  round  its  axis,  the 
brightness  of  the  sky  was  restored,  the  clouds  becoming  dark  through 
contrast  with  this  brightness.  Experiments  of  this  kind  prove  that 
the  blue  light  sent  to  us  by  the  firmament  is  polarized,  and  that  the 
direction  of  most  perfect  polarization  is  perpendicular  to  the  solar 
rays.  Were  the  heavenly  azure  like  the  light  scattered  from  a  thick 
cloud,  the  turning  of  the  prism  would  have  no  effect  upon  it ;  it  would 
be  transmitted  equally  during  the  entire  rotation  of  the  prism.  The 
light  of  the  sky  is  in  great  part  quenched,  because  it  is  in  great  part 
polarized."  This  quotation  forms  part  of  a  very  interesting  dis- 
course on  the  Structure  and  Light  of  Vie  Sky.  See  "  Fragments 
of  Science,"  Chapter  X. 

When  a  plate  of  quartz,  or  a  solution  of  sugar  enclosed  in  a  tube 
with  glass  ends,  is  placed  between  two  crossed  Nicols,  there  is  a 
partial  restoration  of  light.     '*  The  action  thus  exerted  by  quartz  or 


[Element*  of  Natural  Philosophy,  p.  549.]  269 

vugar  is  called  rotation  of  the  plane  of  polarization,  a  name  which 
precisely  expresses  the  observed  phenomena."  A  solution  of  l«mf- 
eugar  turns  the  plane  of  i>olarization  in  one  direction  called  right, 
handed;  hence  the  chemical  name  of  such  sugar,  destrote.  A  soln- 
tion  of  grape-sugar  produces  a  left  handed  rotation  of  the  plane  of 
}M)larization  ;  hence  its  chemical  name,  levulose.  (See  Dcsehanei's 
Nat.  Philoe.,  §§  838,  839.)  Among  the  latest  studies  in  this  field  is 
ihat  described  in  the  following  extract  from  Nature,  No.  4!»2  : 

"  rt  is  known  that  Faraday  did  not  succeed  in  proving  electro 
magnetic  rotation  of  the  plane  of  polarization  of  light  in  gases,  nor 
have  others  succeeded.  Considering  the  interest  attaching  to  this 
question,  Herr  Kundt  and  Herr  Rontgen  lately  thought  to  repeat  the 
attempt  with  very  strong  currents  and  under  the  most  favorable 
conditions.  The  result  is  that  they  have  been  able  to  prove  the  rota- 
tion, at  least  in  the  case  of  sulphide  of  carbon  vapor. 

"  Sulphide  of  carbon  was  chosen,  on  the  one  hand,  because  it  shows 
a  strong  electro-magnetic  rotation  in  the  liquid  state,  and  on  the 
other,  its  vapor  has  a  considerable  tension,  even  at  low  temperatures. 
An  iron  tube  was  used  for  enclosure  and  heating  of  the  substancu; 
it  was  closed  at  the  two  ends  with  glass  plates  1  cut.  thick,  and  itself 
enclosed  in  a  tin-plate  tube  ;  so  that  steam  could  be  led  between  the 
tubes  to  heat  the  inner  tube  throughout  to  100°  C.  The  outer  tube 
was  surrounded  by  six  large  wire  coils,  each  having  400  windings  of 
wire  3  mm.  thick,  through  which  was  passed  the  current  from  64 
large  Bunsen  elements.  A  little  sulphide  of  carbon  was  introduced 
into  the  inner  tul>e,  and  the  air  having  been  driven  out  by  vapor 
forming  at  the  ordinary  temperature,  the  tube  was  closed  and  fixed 
in  position,  and  steam  was  sent  through  the  space  round  it. 

"When  the  whole  tube  had  taken  the  temperature  of  l>oiling 
water,  the  glass  plates  and  the  sulphide  of  carbon  vapor  within 
became  quite  transparent.  A  beam  of  light  rectilinearly  polarized 
Ly  a  Nicol  was  now  sent  through,  and  a  Nicol  at  the  other  end  extin- 
guished it.  The  current  of  the  64  elements  being  now  allowed  to 
flow,  a  distinct  brightening  of  the  field  was  observed.  The  brighten 
ing  became  still  greater  when,  after  closing  the  circuit,  the  foremost 
Nicol  was  turned  to  darkness  and  the  current  then  reversed  with  a 
commutator.  The  rotation  of  the  plane  of  polarization  occurred,  as 
was  to  be  expected,  in  the  direction  in  which  the  positive  current 
passed  through  the  wire  coils. 

"  To  test  whether  the  rotation  might  not  be  due  wholly  or  in  part 
to  the  glass  plates  closing  the  inner  tube,  the  experiment  was  ma<le 
without  any  sulphide  of  carbon  in  this  tube.  A  weak  rotation  due 
to  the  glass  was  indeed  observed,  much  smaller  than  in  the  other 


270  [Elements  of  Natural  Philosophy,  pp.  549-552.} 

case.  To  avoid  this,  however,  as  much  as  possible,  the  wire  coils 
next  the  glass  plates  were  shut  out  from  the  circuit.  The  four  coils 
now  traversed  by  the  current  were  so  far  from  the  plates  that  their 
influence  must  have  been  very  small ;  indeed,  the  plates  then  gave 
no  perceptible  rotation.  Sulphide  of  carbon  having  been  again  ad- 
mitted, and  the  experiment  repeated,  there  was  a  well-marked 
brightening,  as  before,  when  the  current  passed.  The  amount  was 
roughly  estimated  at  half  a  degree. 

"It  is  thus  proved  that  saturated  sulphide  of  carbon  vapor  at 
about  100°  C,  in  the  magnetic  field,  rotates  the  plane  of  polarization 
of  light.  Sulphuric  ether  was  tried  in  the  same  way,  but  gave  no 
effect." 

A  more  recent  discussion  of  the  rotation  of  the  plane  of 
polarization  may  be  found  in  Stokes's  "Light  as  a  Means 
of  Investigation,"  at  p.  25. 

The  author  is  obliged,  reluctantly,  to  leave  this  topic  at 
this  point.  If  you  are  interested  in  it,  he  would  refer  you 
to  Deschanel's  "Natural  Philosophy,"  Chap.  LXV.;  Lom- 
mel's  "Nature  of  Light,"  Chapter  XXII.  to  XXV.;  Tyn- 
dall's"  Notes  on  Light  and  Electricity,"  §§405  to  502; 
Spottiswoode's  "  Polarization  of  Light "  and  to  Gordon's 
"Electric  Induction,"  pp.  127-138. 

§  745  (a).  By  giving  to  the  selenite  proper  shapes  and 
thicknesses,  colored  figures  of  flowers,  butterflies,  etc., 
have  been  produced.  If,  when  the  field  is  thus  colored, 
the  analyzer  be  turned  upon  its  axis  90°,  the  colors  will  be 
changed  to  their  complementary  colors. 

§  746.  See  Daniell's  "  Principles  of  Physics,"  p.  443  and 
Deschanel's  "Natural  Philosophy,"  §§  359-361,  C. 

§  747.  "  Although,  in  a  strictly  mechanical  sense,  there  is  a  con- 
servation of  energy,  yet,  as  regards  usefulness  or  fitness  for  living 
beings,  the  energy  of  the  universe  is  in  process  of  deterioration. 
Universally  diffused  heat  forms  what  we  may  call  the  great  waste- 
heap  of  the  universe,  and  this  is  growing  larger  year  by  year.  At 
present,  it  does  not  sensibly  obtrude  itself,  but  who  knows  that  the 
time  may  not  arrive  when  we  shall  be  practically  conscious  of  its 
growing  bigness  ? 

"We  have  regarded  the  universe,  not  as  a  collection  of  matter, 
but  rather  as  an  energetic  agent — in  fact,  as  a  lamp.     Now  it  has 


[Element*  of  Natural  Philosophy,  pp.  552-657.]  tf\ 

been  pointed  out  by  Thomson,  that  looked  at  in  this  light,  the  uni 
verse  is  a  system  that  had  a  beginning  and  must  have  an  end  ;  for  a 
process  of  degradation  cannot  be  eternal.  If  we  could  view  tin- 
universe  as  a  candle  not  lit,  then  it  is  perhaps  conceivable  to  regard 
it  as  having  been  always  in  existence  ;  but  if  we  regard  it  rather  as 
a  candle  that  has  been  lit,  we  become  absolutely  certain  that  it  can- 
not have  been  burning  from  eternity  and  that  a  time  will  come  when 
it  will  cease  to  burn.  We  are  led  to  look  to  a  beginning  in  which 
I  he  particles  of  matter  were  in  a  diffuse,  chaotic  state,  but  endowed 
with  the  power  of  gravitation,  and  we  are  led  to  look  to  an  eud  in 
which  the  whole  universe  will  be  one  equally  heated,  inert  mass  and 
trom  which  everything  like  life  or  motion  or  beauty  will  have  utterly 
gone  away." — Balfour  Stewart. 

General  Review,  Page  555. 

7.  (c.)  144.72  ft.— ^ns. 

8.  (c.)  117.3  ft.  or  35.7588  m.—Am. 

13.  (a.)  2.76;  (b.)  Thesecond;  (c.)  The  third;  (d.)  To 
gain  velocity. 

14.  8  =  i  gP  =  16.08  ft.  x  7i  X  7J  =  904.5  ft 

16.  It  makes  no  difference  what  it  strikes.     See  §  157. 
K    F    -   «"*  -  32  x  213  x  213  _ 

number  of  grammeters.     The  energy  is   74.071836   kilo- 
gram meters. 

A  still  better  solution  is  the  following: 

K.  E.  =  fr*  =  88x21,800x21,800  =  W0400(K)> 

til 

the  number  of  ergs. 

17.  (b.)  16.08  ft.  x  GJ-  x  6£  =  679.38  tt—Ans. 
(c.)  16.08  ft.  x  17  =  273.36  ft.—  An*. 

(d.)  v  as  gt\  448  =  32.16tf;  /  =  13.9  + 

Arts.,  13.9-+-  seconds. 

22.   I-)   ?=  jT£=,  the  part  that  the  remaining  air  is  of 

that  originally  in  Hie  receiver.     The  tension  is  fff  of  one 
atmosphere.     See  §  289  and  Ex.  7.  p.  180. 

83.   02.42  lb.   x  150  x  20  x  10  =  1,872,600  lbr^-4fw. 
(§23.1.) 


272  [Elements  of  Natural  Philosophy,  pp.  557,  558.] 

25.  (a.)  Because  the  atmospheric  pressure  is  not  great 
enough  to  support  such  a  column  of  water. 

(b.)  The  piston  should  be  lowered  to  within  28  feet 
of  the  surface  of  the  water. 

28.  |  of  surface  weight  =  120  lb.;   surface  weight  = 

320  lb*     320  =  4'   l!  =  I)  4000  mi-  x  2  =  8000  mi-> 

the  distance  from  the  earth's  centre.     Ans.,  4000  mi. 

39.  (a.)  (1.12  x  50)  +  1090  =  1146;  1146  ft.  x  18  = 
20,628  ft.  or  4  miles  nearly. — Ans. 

(b.)  180;  216;  288. 

40.  (a.)  It  contains  \  cubic  meter  of  water,  or  500  liters, 
which  weigh  500  Kg. — Ans. 

(b.)  100  cu.  cm.    x    50  x  25  =  125000  cu.  cm.  = 
125  l  of  water  which  weigh  125  Kg. 


4L  (*•>  ^W^~^T=  U'  thenumber  of  horse-P<™*- 

4 

42.  On  p.  147  of  the  text-book,  we  find  the  formula, 
v  =  V%g$ ;    v2  =  2gS.     Substituting  this  value, 
vn?  _  ZgSw  ==wS=26       528Q  _  132ooo,  the  number 

of  foot-pounds. — Ans.    See  solution  of  7th,  page  361. 
43'  302 !  20^ }  "  441  ••  576    .-.  x  =  73H    Ans.,  73ff  lb. 

44.  Its  diameter  is  9  times  that  of  the  earth.  Since 
solids  are  proportioned  to  the  cubes  of  their  like  dimen- 
sions, Saturn  in  (9  x  9  x  9  =)  729  times  as  large  as  the 
earth.  But  it  is  only  .12  as  dense;  hence,  its  mass  is 
(729  x  .12  =)  87.48  times  that  of  the  earth. 

1  V^'v    |  =  16'08  :x;    •'*  X  =  17*3664- 

Ans.,  17.36+  ft. 


[humerus  of  Natural  Philosophy,  pp.  oo'j,50u.]        273 

„     .    fc  150x1,920  x  1,'J.*" 

6L  <*>  64.32  x  772^2,000  =  5'°  +  ' 

32  +  5.5  ^  3T.5.— A  us.,  37±°  F. 
52.  (a.)  50  —  32  =  18. 

18  x  #    =  10.— Arts.,  10°  C. 
(c.)  Potential  energy  of  chemical  separation  in  fuel 
and  atmospheric  oxygen  ;  heat;  mechanical  kinetic  energy 
of  moving  train ;  heat  developed  by  friction. 

63.  1,390  x  30.48  =  42,367.2,  the  number  of  grain- 
centimeters.     See  §  1*54. 

980  x  42,367.2  =  41,519,856,  the  number  of  ergs. 

55.  (a.)  With  less  difficulty.    See  §§  622-0 M. 

56.  (a.)  See  §  658  (a). 

59.  (a. )  It  transmits  only  red  light,  (b.)  It  reflects  only 
red  light. 

62.  (b.)  See  §  35;  440  lb.  =  200  Kg.  A  liter  of  air 
weighs  0.0896  #.  x  14.42'  s=  1.292032  g.  The  difference 
between  the  weight  of  a  liter  of  hydrogen  and  that  of  the 
air  it  displaces  (1.292032  #.  —  .0896  #.  =  1.202432  #.)  is 
the  lifting  power  of  a  liter  of  hydrogen.  The  lifting  power 
required  is  200,000  #.  200,000  g.-r- 1.202432 #.=166,329.5+, 
the  number  of  liters.     See  Appendix  G. 

Ans.,  166.3295  A7. 


63. 


(a.)  15  lb.  x    (jtf  =  2.54  lb.— Ans.     See  §  289. 


(b.)  8  =  yP  =  16.08  ft.  x  6±  x  6i  =  679.38.  ft. 
— Ans. 

64.  (a.)  The  boat  displaced  equal  quantities  of  fresh  and 
of  salt  water.  Let  x  =  the  weight  of  fresh  water  dis- 
placed =  weight  of  the  river  cargo.  1.028  x  =  the  weight 
of  stilt  water  displaced  =  weight  of  the  ocean  cargo. 
.028  x  =  44,800  lb.  x  =  1,600,000  lb.— Ans. 

(b.)  The  water  is  5  times  as  heavy  ;  an  equal  bulk 
of  water  weighs  60  lb.;  60  lb.  —  12  lb.  =  48  lb.—  Am. 


274  [Elements  of  Natural  Philosophy,  pp.  560-569.] 

65.  (a.)  See  §  475.     9  x  140  =  1,260,  the  number  of 
watts. 

1260  -j-  746  =  1.69  nearly,  the  number  of  H.  P. 
(b.)  See  §  228.  24  x  170  x  12  =  48,960,  the  num- 
ber of  cu.  in.  in  "the  imaginary  column."  This  is  28 J 
cu.  ft.  See  Note,  p.  124.  62.42  lb.  x  28£  =  1,768.57  lb. 
This  is  the  total  load  supported  by  water  pressure  including 
the  piston  and  its  head. 

66.  424  grammeters  =  42,400  gram-centimeters.     See 
§  154.     980  ergs  x  42,400  =  41,552,000  ergs. 


Appendix  D.  The 
accompanying  figure 
illustrates  the  method 
of  performing  this 
pretty  experiment.  It 
is  well  to  place  the 
bottle  on  a  plate  be- 
fore breaking  off  the 
tip  of  the  "  drop." 

Appendix  L.  See  Frick's  "Physical  Technics,"  p.  360 
(§§307,308). 

Appendix  M.  See  Frick's  "Physical  Technics,"  p.  365 
(§§  310-312).  Concerning  the  polarization  of  resistance 
coils,  see  "Science,"  Vol.  9,  p.  12. 

Appendix  K  (4).  An  illustrated  description  of  the  ex- 
periment on  the  varying  electrical  resistance  of  selenium 
will  be  found  on  p.  139  of  Gordon's  "  Electric  Induction." 


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